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Parameters Estimation Based on Progressively Censored Data from Inverse Weibull Distribution
Mostafa M. MohieEl-Din,
Fathy H. Riad,
Mohamed A. El-Sayed
Issue:
Volume 2, Issue 6, November 2013
Pages:
149-153
Received:
4 September 2013
Published:
30 September 2013
Abstract: In this article, our main aim is to investigate the parameters estimation of inverse Weibull distribution in the frame work of progressively type II. We consider the censored sample from a two parameters inverse Weibull. The point estimators of the parameters derived by using the maximum likelihood method. The exact joint confidence region and confidence interval for the parameters are obtained. A numerical example is provided to illustrate the proposed. estimation methods developed here.
Abstract: In this article, our main aim is to investigate the parameters estimation of inverse Weibull distribution in the frame work of progressively type II. We consider the censored sample from a two parameters inverse Weibull. The point estimators of the parameters derived by using the maximum likelihood method. The exact joint confidence region and conf...
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Estimate of Subject Specific Index of Relative Performance in ‘K’ Samples
Oyeka Ikewelugo Cyprian Anaene,
Okeh Uchechukwu Marius
Issue:
Volume 2, Issue 6, November 2013
Pages:
154-165
Received:
18 September 2013
Published:
20 October 2013
Abstract: This paper proposes and develops a statistic here termed the ‘relative performance index’ or the index of relative performance’ by subjects both within and between several sampled populations for preferentially rank-ordering subjects by their relative performance in comparison with other subjects from these populations involved in a test or contest. The proposed index would enable decisions on the preferential selection of subjects both within and between various classifications for management purposes. The proposed method enables the estimation of the median and other tiles of not only each of the sampled populations but also the common median of the several populations as functions of the relative performance indices. The method unlike some other methods used for the analysis of many samples is based mostly on individual subjects rather than on only summary indices or averages. Test statistics also based on subject specific relative performance indices are developed to test desired hypothesis concerning population. The proposed indices being subject specific rather than merely summary averages easily enables one to more clearly and succinctly examine individual subjects relative performance or level of seriousness in a condition in comparison with other subjects from the sampled populations thereby providing subject targeted information to better guide any interventionist actions on a condition of research interest. The method is illustrated with some data and shown to compare favorably with some existing methods.
Abstract: This paper proposes and develops a statistic here termed the ‘relative performance index’ or the index of relative performance’ by subjects both within and between several sampled populations for preferentially rank-ordering subjects by their relative performance in comparison with other subjects from these populations involved in a test or contest...
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Method of Principal Factors Estimation of Optimal Number of Factors: An Information Criteria Approach
Nwosu Dozie. F.,
Onyeagu Sidney. I.,
Osuji George A.
Issue:
Volume 2, Issue 6, November 2013
Pages:
166-175
Received:
24 September 2013
Published:
30 October 2013
Abstract: The issue of the number of factors to be retained in a factor analysis has been an undefined. Be that as it may, this paper tries to x-ray the number of factors (k) to be retained in a factor analysis for different sample sizes using the method of Principal Factor estimation when the number of variables are ten (10). Stimulated data were used for sample sizes of 30, 50 and 70 and the Akaike Information Criterion (AIC), the Schwarz Information Criterion (SIC) and the Hannan Quinne Information Criterion (HQIC) values were obtained when the number of factors(k) are two, three, and five (2,3 and 5). It was discorvered that the AIC, SIC, and HQIC values are smallest when k = 5, and highest when k = 2 for the sample sizes of 30 and 70. But, for a sample of 50, the values of these information criteria is smallest for k = 3, highest for k=5. Hence, conclusion is drawn that for the sample sizes of 30 and 70, the optimal number of factors to retain is 5 and 3 for the sample size of 70. This implies that, the number of factors to retain is a function of the sample size of the data.
Abstract: The issue of the number of factors to be retained in a factor analysis has been an undefined. Be that as it may, this paper tries to x-ray the number of factors (k) to be retained in a factor analysis for different sample sizes using the method of Principal Factor estimation when the number of variables are ten (10). Stimulated data were used for s...
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Application of Multivariate Methods for Assessment of Variations in Rivers/Streams Water Quality in Niger State, Nigeria
Audu Isah,
Usman Abdullahi,
Muhammed Muhammed Ndamitso
Issue:
Volume 2, Issue 6, November 2013
Pages:
176-183
Received:
25 September 2013
Published:
10 November 2013
Abstract: Multivariate statistical methods, Cluster Analysis (CA) and Canonical Discriminant Analysis (CDA) were applied to assess the temporal and spatial variations, and identify pollution sources in some rivers/streams of Niger State in Nigeria. Sixteen towns were sampled as medium-sized towns in which data were gathered on four physical, eleven chemical and two microbial parameters of water. Hierarchical CA grouped the sixteen sampled sites into four main seasonal clusters and three main groups of similar water quality. Stepwise selection for the temporal Discriminant Analysis (DA) identified the most significant parameters for discriminating between the four seasons as magnesium, Escherichia coli, total coliform, total dissolved solid (TDS) and total hardness with 83.3% apparent correct classification. The stepwise selection for the spatial Discriminant Analysis (DA) show that, Escherichia coli and magnesium is more prevalent in winter; while Escherichia coli and total dissolved solid (TDS) is higher in spring; and Escherichia coli and total coliform were more in summer and autumn with 94% total success rate of classification. The outcome of this study also show that the sources of water in groups one and two were more polluted than group three during summer and autumn than in the winter and spring. Based on these findings, it is recommended that the frequency of monitoring sites could be reduced to only sites in groups one and two while the seasons could be based on summer and autumn.
Abstract: Multivariate statistical methods, Cluster Analysis (CA) and Canonical Discriminant Analysis (CDA) were applied to assess the temporal and spatial variations, and identify pollution sources in some rivers/streams of Niger State in Nigeria. Sixteen towns were sampled as medium-sized towns in which data were gathered on four physical, eleven chemical ...
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Assessing the Knowledge, Attitude and Factors Affecting Team Building Amongst Health Workers in Nigeria Using the Permutation Method for Hotelling T-squared Analysis
Aronu,
C. O.,
Bilesanmi,
A. O.
Issue:
Volume 2, Issue 6, November 2013
Pages:
184-190
Received:
2 October 2013
Published:
10 November 2013
Abstract: This study is on assessing the knowledge, attitude and factors affecting team building activities amongst health workers in Nigeria. The objective of this study is to determine the equality on knowledge and attitude of team building activities between health workers of Anambra state and Delta State. The source of data for this study was questionnaire, administered randomly to a sample of 200 workers at Anambra State and a sample of 305 workers at the Delta State. The test statistic used was the permutation method for Hotelling T –squared. The result of the analysis showed that there exist a significant difference on knowledge, attitude and factors affecting team building in Anambra State and Delta State with a test statistic value of 8073.7 and a p-value of 0.00 for 10, 000 permutations. This result indicate that the obtained significant value of 0.00 fall on the rejection region of the hypothesis assuming a significance level of 5% (α = 0.05) and implies that there is significant difference on the knowledge, attitude and factors affecting team building in the two States. Suggestion for the management of health in Anambra State to encourage the practice of team building by either sponsoring training of staff on team building or organizing seminars that will enhance the practice of team building was made since as argued in the present study that the benefit of team building in any organization is to achieves cohesiveness, improve the team attitude, effectiveness and enhances productivity. Studies on assessing the knowledge, attitude and factors affecting team building in other professional sector such as education, finance and environment in Nigeria is seen as an area for future research.
Abstract: This study is on assessing the knowledge, attitude and factors affecting team building activities amongst health workers in Nigeria. The objective of this study is to determine the equality on knowledge and attitude of team building activities between health workers of Anambra state and Delta State. The source of data for this study was questionnai...
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Method of Maximum Likelihood Estimation of Optimal Number of Factors: An Information Criteria Approach
Nwosu F. Dozie,
Onyeagu,
Sidney I.,
Osuji,
George A.,
Ekezie Dan Dan
Issue:
Volume 2, Issue 6, November 2013
Pages:
191-201
Received:
25 September 2013
Published:
10 November 2013
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Comparative Study on Forecasting Accuracy among Moving Average Models with Simulation and PALTEL Stock Market Data in Palestine
Samir K. Safi,
Issam A. Dawoud
Issue:
Volume 2, Issue 6, November 2013
Pages:
202-209
Received:
9 October 2013
Published:
10 November 2013
Abstract: In this paper, we discuss three analytical time series models for selecting the more effective with an accurate forecasting models, among others. We analytically modify the stochastic realization utilizing (i) k-th moving average, (ii) k-th weighted moving average, and (iii) k-th exponential weighted moving average processes. The examining methods have been applied for 1000 independent datasets for five different parameters with possible orders . We consider stationary data , and non-stationary data with first and second differences for ARIMA models. We consider short term and long term, observations. A similar forecasting models was developed and evaluated for the daily closing price of Stock Price of the PALTEL company in Palestine. The main finding is that, in most simulated datasets one or more of the proposed models give better forecast accuracy than the classical model (ARIMA). Specially, in most simulated datasets 3– time Exponential Weighted Moving Average based on Autoregressive Integrated Moving Average (EWMA3-ARIMA) is the best forecasting model among all other models. For PALTEL Stock Price, the best forecasting model is 3–time Moving Average based on Autoregressive Integrated Moving Average (MA3-ARIMA) among all other models.
Abstract: In this paper, we discuss three analytical time series models for selecting the more effective with an accurate forecasting models, among others. We analytically modify the stochastic realization utilizing (i) k-th moving average, (ii) k-th weighted moving average, and (iii) k-th exponential weighted moving average processes. The examining methods...
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Multivariate Analysis of Data on the Effects of Different Vegetative Covers on Some Physical Properties of a Selected Nigerian Soil
CHUKWUDI JUSTIN OGBONNA,
OPARA JUDE,
HYCINTH CHUKWUDI IWU
Issue:
Volume 2, Issue 6, November 2013
Pages:
210-220
Received:
22 October 2013
Published:
10 November 2013
Abstract: This work discusses the use of multivariate analysis of variance to tackle the problem of investigating the effects of different vegetative covers on the physical properties of a selected Nigerian soil. An additive effect model was assumed and using data obtained from the Department of Soil Science of the University of Nigeria, Nsukka, we tested for the equality of significant treatment effects. The result of the analysis revealed that the treatment effects were found to be significant being acceptable at 5 percent level. Based on our analysis, we recommended that the vegetative covers in question are useful and necessary and therefore should be used to improve the soil physical conditions for any overused land in Nsukka area of Nigeria and similar soils elsewhere not in Nsukka depending on the use and type of farming system the land is put to.
Abstract: This work discusses the use of multivariate analysis of variance to tackle the problem of investigating the effects of different vegetative covers on the physical properties of a selected Nigerian soil. An additive effect model was assumed and using data obtained from the Department of Soil Science of the University of Nigeria, Nsukka, we tested fo...
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Estimating the Fisher’s Scoring Matrix Formula from Logistic Model
Issue:
Volume 2, Issue 6, November 2013
Pages:
221-227
Received:
21 October 2013
Published:
20 November 2013
Abstract: This paper proposes a matrix approach to estimating parameters of logistic regression with a view to estimating the effects of risk factors of gestational diabetic mellitus (GDM). The proposed method of maximum likelihood estimation (MLE) unlike other methods of estimating parameters of non-linear regression is simpler and convergence of parameters is quicker. The odds ratio obtained from the logistic regression were used to interpret the effects of these risk factors on GDM where obesity and F.H as risk factors, were positively associated with GDM. The proposed method was seen to compare favorably with other known methods.
Abstract: This paper proposes a matrix approach to estimating parameters of logistic regression with a view to estimating the effects of risk factors of gestational diabetic mellitus (GDM). The proposed method of maximum likelihood estimation (MLE) unlike other methods of estimating parameters of non-linear regression is simpler and convergence of parameters...
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Statistical Analysis of Life-Time and Temperature of Black Holes
Ved Prakash,
Dipo Mahto,
Ashok Kumar,
Basant Kumar Das
Issue:
Volume 2, Issue 6, November 2013
Pages:
228-232
Received:
4 November 2013
Published:
30 November 2013
Abstract: In the present article, statistical analysis of lifetime and temperature of the black holes have been studied existing in X-ray binaries and active galactic nuclei with the help of formula Г = (M/Mʘ)3 x 1066 years and T=hc3/8πkGM Kelvin respectively where M stands for the mass of black hole and other parameters have their usual meaning.
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Comparison of Statistical Methods for Outlier Detection in Proficiency Testing Data on Analysis of Lead in Aqueous Solution
Sushree Swarupa Tripathy,
Rajiv Kumar Saxena,
Prabhat Kumar Gupta
Issue:
Volume 2, Issue 6, November 2013
Pages:
233-242
Received:
5 November 2013
Published:
10 December 2013
Abstract: Proficiency testing is the regular testing of the performance of individual laboratories by an external agency. Stable and effectively homogeneous elemental solutions of different concentrations ranging were prepared at NPL and were certified by round robin test. These certified reference materials (CRMs) along with reports containing all information, where the laboratories were identified only by a reference number were being distributed to sixty seven participant laboratories. In this paper the data of lead (Pb) elemental solution of 1-5 mg/l is only presented for outlier detection. The results received from the sixty four numbers of laboratories for Pb elemental solution statistically evaluated with different approaches viz. Cochran’s test, Grubb’s test, Hampel’s test, classical z-score, median and NIQR method, robust statistical analysis : Algorithm A (ISO 13528) and NATA method. The robust estimate of average and uncertainty values derived from ISO 13528 method are very close to the reference value for the 1 and 2 mg/l of Pb elemental solutions. The performance of the laboratories was expressed by z-score and the laboratories having z< 2 are classified as satisfactory, 2 < z < 3 are classified as questionable and z> 3 are considered as unsatisfactory. Among all the methods, the highest number of outlier i.e. about 30 % obtained by NATA statistical analysis. As NATA method considers variance in both within and between laboratory results so it seems to be the most suitable method for outlier detection for the present data set evaluated in this study.
Abstract: Proficiency testing is the regular testing of the performance of individual laboratories by an external agency. Stable and effectively homogeneous elemental solutions of different concentrations ranging were prepared at NPL and were certified by round robin test. These certified reference materials (CRMs) along with reports containing all informati...
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Phenol Removal via Advanced Oxidative Processes (O3/Photo-Fenton) and Chemometrics
Ana Paula Barbosa Rodrigues de Freitas,
Leandro Valim de Freitas,
Hélcio José Izário Filho,
Messias Borges Silva
Issue:
Volume 2, Issue 6, November 2013
Pages:
243-247
Received:
7 November 2013
Published:
10 December 2013
Abstract: Taguchi’s L16 orthogonal array in the study of removal of total phenols using advanced oxidation processes was efficient. In the statistical assessment, the input variables obtained as significant through ANOVA were: hydrogen peroxide (F = 10.0924 and p-value = 5.02) and ozone (F = 3.8686 and p-value = 14.39). In this assessment, the best experimental condition for the removal of total phenols is 100%. The following factors must therefore be adjusted: hydrogen peroxide = 38, 7g and ozone flow = 3 L/h.
Abstract: Taguchi’s L16 orthogonal array in the study of removal of total phenols using advanced oxidation processes was efficient. In the statistical assessment, the input variables obtained as significant through ANOVA were: hydrogen peroxide (F = 10.0924 and p-value = 5.02) and ozone (F = 3.8686 and p-value = 14.39). In this assessment, the best experimen...
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A Comparative Study between Ridit and Modified Ridit Analysis
Ebuh Godday Uwawunkonye,
Oyeka Ikewelugo Cyprian Anaene
Issue:
Volume 2, Issue 6, November 2013
Pages:
248-254
Received:
2 November 2013
Published:
10 December 2013
Abstract: This paper compares ridit analysis with modified ridit analysis. The comparison was then illustrated with an example. It was observed from the example at least, that when the sample sizes of the two samples being compared are too disparate, a more reliable conclusion using the Bross ridit analysis is likely to be reached only when the group with the larger sample size is used as the reference group. Otherwise Bross ridit analysis would lead to conflicting conclusions, depending on which group is used as the reference group. Modified ridit analysis treats the groups being studied as samples drawn from some larger populations in which the variances or standard deviations as well as the results obtained are the same no matter which sample is used as the reference group. The modified procedure is therefore preferable to ridit analysis especially in cases where the groups being compared are samples from some populations.
Abstract: This paper compares ridit analysis with modified ridit analysis. The comparison was then illustrated with an example. It was observed from the example at least, that when the sample sizes of the two samples being compared are too disparate, a more reliable conclusion using the Bross ridit analysis is likely to be reached only when the group with th...
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Investigating Predictors of Examination Result Data Using Logistic Regression (A Case Study of Imo State Polytechnic, Umuagwo, Imo State, Nigeria)
Opara Jude,
Esemokumo Perewarebo Akpos,
Iheagwara Andrew Ihuoma,
Okenwe Idochi,
OSUJI GEORGE A.
Issue:
Volume 2, Issue 6, November 2013
Pages:
255-267
Received:
5 December 2013
Published:
20 December 2013
Abstract: This study tends to analyze the school examination results (scores) of 300 randomly selected students of Imo State Polytechnic, Umuagwo near Owerri, Imo State, Nigeria who offer English Language and Mathematics as general courses, using the binary logistic regression model with the aim of examining how some factors (variables) in secondary school level contribute to the performance of the students in the Polytechnic. The analysis is performed on the basis of the explanatory variables viz; gender, type of secondary schools, category of secondary schools, board of examinations and location of secondary schools, where scores of students in English Language and Mathematics are assumed to be the response variables. Applying the method of Correspondence Analysis revealed that there exist a significant correlation between board of examinations and location of schools, which made the analysis to be into two stages. The first stage is based on using English Language and Mathematics as a response variable with gender, type of secondary schools, category of secondary schools, and board of examinations as the explanatory variables. The second stage, on the other hand, English Language and Mathematics is the response variable, while gender, type of secondary schools, category of secondary schools, and location of schools are the explanatory variables. The odds ratio analysis compares the scores obtained in two examinations viz English language and Mathematics. The result of the analysis revealed that females are always showing best performances in Mathematics than English examination in all the two stages carried out in this paper. The study also showed that performances of students from girls’ schools are found to be the best in English Language course examination than those of students from boys; secondary schools. Furthermore, the study revealed that government schools always show better performance in English course examination than in Mathematics.
Abstract: This study tends to analyze the school examination results (scores) of 300 randomly selected students of Imo State Polytechnic, Umuagwo near Owerri, Imo State, Nigeria who offer English Language and Mathematics as general courses, using the binary logistic regression model with the aim of examining how some factors (variables) in secondary school l...
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Derivation of Inflection Points of Nonlinear Regression Curves - Implications to Statistics
Ayele Taye Goshu,
Purnachandra Rao Koya
Issue:
Volume 2, Issue 6, November 2013
Pages:
268-272
Received:
19 December 2013
Published:
10 January 2014
Abstract: In this paper, we derive inflection points for the commonly known growth curves, namely, generalized logistic, Richards, Von Bertalanffy, Brody, logistic, Gompertz, generalized Weibull, Weibull, Monomolecular and Mitscherlich functions. The functions often represent the mean part of non-linear regression models in Statistics. Inflection point of a growth curve is the point on the curve at which the rate of growth gets maximum value and it represents an important physical interpretation in the respective application area. Not only the model parameters but also the inflection point of a growth curve is of high statistical interests.
Abstract: In this paper, we derive inflection points for the commonly known growth curves, namely, generalized logistic, Richards, Von Bertalanffy, Brody, logistic, Gompertz, generalized Weibull, Weibull, Monomolecular and Mitscherlich functions. The functions often represent the mean part of non-linear regression models in Statistics. Inflection point of a ...
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Intrinsically Ties Adjusted Tau (C-Tat) Correlation Coefficient
OYEKA CYPRIL ANENE,
OSUJI GEORGE AMAEZE,
NWANKWO CHRISTIAN CHUKWUEMEKA
Issue:
Volume 2, Issue 6, November 2013
Pages:
273-281
Received:
23 November 2013
Published:
10 January 2014
Abstract: This paper proposes a method for correcting and adjusting the usual or regular estimates of Tau correlation coefficients for the possibility of ties within and between observations in the population being correlated. The index here called C-Tat for ‘ties adjusted Tau correlation coefficient’ is formulated to intrinsically and structurally adjust and correct the estimated Tau correlation coefficient for the possible presence of tied observations in the sampled populations and for the fact that the estimates obtained are often dependent on, that is, vary depending on which of the two populations under study has its assigned ranks arranged in their natural order and which has its assigned ranks arranged in their natural order and which has its assigned ranks tagged along. The proposed method is illustrated with some sample data and shown to yield more reliable and efficient estimates of tau correlation coefficients than the usual method which is able to give the same estimates only if there are no tied observations what-so-ever in the sampled populations.
Abstract: This paper proposes a method for correcting and adjusting the usual or regular estimates of Tau correlation coefficients for the possibility of ties within and between observations in the population being correlated. The index here called C-Tat for ‘ties adjusted Tau correlation coefficient’ is formulated to intrinsically and structurally adjust an...
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Graphical and Queuing Model of Banking Operations in Intercontinental Bank Plc, Nigeria
Hycinth Chukwudi Iwu,
Chukwudi Justin Ogbonna,
Opara Jude
Issue:
Volume 2, Issue 6, November 2013
Pages:
282-292
Received:
21 December 2013
Published:
10 January 2014
Abstract: This study is aimed at modeling the influence and network relationship existing amongst members of staff of commercial banks. It also solved the problem of profit maximization through staff reduction in a commercial banking system. In this paper, graph and queuing theories were applied in achieving the smooth running of the operations in a commercial bank using Intercontinental bank plc as a case study.
Abstract: This study is aimed at modeling the influence and network relationship existing amongst members of staff of commercial banks. It also solved the problem of profit maximization through staff reduction in a commercial banking system. In this paper, graph and queuing theories were applied in achieving the smooth running of the operations in a commerci...
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A New Criterion for Lag-Length Selection in Unit Root Tests
Agunloye,
Oluokun Kasali,
Arnab,
Raghunath,
Shangodoyin,
Dahud Kehinde
Issue:
Volume 2, Issue 6, November 2013
Pages:
293-298
Published:
30 January 2014
Abstract: This paper examines lag selection problem in unit root tests which has become a major specification problem in empirical analysis of non-stationary time series data. It is known that the implementation of unit root tests requires the choice of optimal truncation lag for good power proper ties and it is equally unrealistic to assume that the true optimal truncation lag is known a prior to the practitioners and other applied researchers. Consequently, these users rely largely on the use of standard information criteria for selection of truncation lag in unit root tests. A number of previous studies have shown that these criteria have problem of over-specification of truncation lag-length leading to the well-known low power problem that is commonly associated with most unit root tests in the literature. This paper focuses on the problem of over-specification of truncation lag-length within the context of augmented Dickey-Fuller (ADF) and generalized least squares Dickey-Fuller (DF-GLS)unit root tests. In an attempt to address this lag selection problem, we propose a new criterion for the selection of truncation lag in unit root tests based on Koyck distributed lag model and we show that this new criterion avoids the problem of over-specification of truncationlag-length that is commonly associated with standard information criteria.
Abstract: This paper examines lag selection problem in unit root tests which has become a major specification problem in empirical analysis of non-stationary time series data. It is known that the implementation of unit root tests requires the choice of optimal truncation lag for good power proper ties and it is equally unrealistic to assume that the true op...
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