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Multivariate Outlier Detection Using Independent Component Analysis
Md. Shamim Reza,
Sabba Ruhi
Issue:
Volume 3, Issue 4, August 2015
Pages:
171-176
Received:
17 May 2015
Accepted:
29 May 2015
Published:
19 June 2015
Abstract: The recent developments by considering a rather unexpected application of the theory of Independent component analysis (ICA) found in outlier detection, data clustering and multivariate data visualization etc. Accurate identification of outliers plays an important role in statistical analysis. If classical statistical models are blindly applied to data containing outliers, the results can be misleading at best. In addition, outliers themselves are often the special points of interest in many practical situations and their identification is the main purpose of the investigation. This paper takes an attempt a new and novel method formultivariate outlier detection using ICA and compares with different outlier detection techniques in the literature.
Abstract: The recent developments by considering a rather unexpected application of the theory of Independent component analysis (ICA) found in outlier detection, data clustering and multivariate data visualization etc. Accurate identification of outliers plays an important role in statistical analysis. If classical statistical models are blindly applied to ...
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Conversely Convergence Theorem of Fabry Gap
Naser Abbasi,
Molood Gorji
Issue:
Volume 3, Issue 4, August 2015
Pages:
177-183
Received:
29 May 2015
Accepted:
10 June 2015
Published:
25 June 2015
Abstract: Our previous paper conducted to prove a variation of the converse of Fabry Gap theorem concerning the location of singularities of Taylor-Dirichlet series, on the boundary of convergence. In the present paper, we prove conversely convergence theorem of Fabry Gap. This is another proof of Fabry Gap theorem. This prove may be of interest in itself.
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Detection of Non-Linearity in the Time Series Using BDS Test
Akintunde,
M. O.,
Oyekunle,
J. O.,
Olalude G. A.
Issue:
Volume 3, Issue 4, August 2015
Pages:
184-187
Received:
7 May 2015
Accepted:
16 June 2015
Published:
6 July 2015
Abstract: The need to determine the status of the series is a very important issue that must be addressed before embarking on the statistical analysis of such series; this paper therefore, examines the status of the commercial bank savings in Nigeria. From the analysis we discovered that at level the series was not stationary as shown in figure 1, however at the first difference (figure 2) the series was stationary, so also the unit root test applied shows that at level the series was not stationary (table 1) but at first difference it was stationary (table 2) and this actually paved way for the application of Brock- Dechert-Scheinkman (table 3) test which actually revealed that this series could be best estimated by the use of non-linear model as the null hypothesis of linearity of the series was out rightly rejected and the alternative was accepted. The importance of this result lies on the fact that it guides against model misspecification as using linear model to estimate the parameter of the non-linear model will result in model judgmental error.
Abstract: The need to determine the status of the series is a very important issue that must be addressed before embarking on the statistical analysis of such series; this paper therefore, examines the status of the commercial bank savings in Nigeria. From the analysis we discovered that at level the series was not stationary as shown in figure 1, however at...
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On One 3-Dimensional Boundary-Value Problem with Inclined Derivatives
Mekhtiyev Magomed Farman,
Aliyev Nihan Alipanah,
Fomina Nina Ilyinichna
Issue:
Volume 3, Issue 4, August 2015
Pages:
188-193
Received:
11 June 2015
Accepted:
7 July 2015
Published:
7 July 2015
Abstract: A boundary-value problem with inclined derivatives in 3-dimensional space with the boundaries – surfaces of Liapunov type is considered in the paper. The method of investigation is based on the necessary conditions. The advantage compared to the theory of potentials is that we don‘t have limit passage, we use boundary values which are obtained from the principal relationships called necessary conditions. Remark that the directions of the derivatives given in the boundary conditions are arbitrary. Tangent directions may be some subset of the given directions.
Abstract: A boundary-value problem with inclined derivatives in 3-dimensional space with the boundaries – surfaces of Liapunov type is considered in the paper. The method of investigation is based on the necessary conditions. The advantage compared to the theory of potentials is that we don‘t have limit passage, we use boundary values which are obtained from...
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Solving Linear Time Varying Systems by Orthonormal Bernstein Polynomials
Issue:
Volume 3, Issue 4, August 2015
Pages:
194-198
Received:
3 May 2015
Accepted:
22 May 2015
Published:
29 July 2015
Abstract: In this paper we present a method to find the solution of time-varying systems using orthonormal Bernstein polynomials. The method is based upon expanding various time functions in the system as their truncated orthonormal Bernstein polynomials. Operational matrix of integration is presented and is utilized to reduce the solution of time-varying systems to the solution of algebraic equations. Illustrative examples are included to demonstrate the validity and applicability of the technique.
Abstract: In this paper we present a method to find the solution of time-varying systems using orthonormal Bernstein polynomials. The method is based upon expanding various time functions in the system as their truncated orthonormal Bernstein polynomials. Operational matrix of integration is presented and is utilized to reduce the solution of time-varying sy...
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The Application of ARIMA Model in 2014 Shanghai Composite Stock Price Index
Renhao Jin,
Sha Wang,
Fang Yan,
Jie Zhu
Issue:
Volume 3, Issue 4, August 2015
Pages:
199-203
Received:
30 June 2015
Accepted:
27 July 2015
Published:
5 August 2015
Abstract: In order to study the changes of Shanghai Composite Stock Price Index (SCSPI) and predict the trend of stock market fluctuations, this paper constructed a time-series analysis．A non-stationary trend is found, and an ARIMA model is found to sufficiently model the data. A short trend of Shanghai composite stock price index is then predicted using the established model.
Abstract: In order to study the changes of Shanghai Composite Stock Price Index (SCSPI) and predict the trend of stock market fluctuations, this paper constructed a time-series analysis．A non-stationary trend is found, and an ARIMA model is found to sufficiently model the data. A short trend of Shanghai composite stock price index is then predicted using the...
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Modeling the Effects of Time Delay on HIV-1 in Vivo Dynamics in the Presence of ARVs
Kirui Wesley,
Rotich Kiplimo Titus,
Bitok Jacob,
Lagat Cheruiyot Robert
Issue:
Volume 3, Issue 4, August 2015
Pages:
204-213
Received:
29 July 2015
Accepted:
8 August 2015
Published:
14 August 2015
Abstract: Mathematical models to describe in vivo and in vitro immunological response to infection in humans by HIV-1 have been of major concern due to the rich variety of parameters affecting its dynamics. In this paper, HIV-1 in vivo dynamics is studied to predict and describe its evolutions in presence of ARVs using delay differential equations. The delay is used to account for the latent period of time that elapsed between HIV – CD4+ T cell binding (infection) and production of infectious virus from this host cell. The model uses four variables: healthy CD4+T-cells (T), infected CD4+T-cells (T*), infectious virus (VI) and noninfectious virus (VN). Of importance is effect of time delay and drug efficacy on stability of disease free and endemic equilibrium points. Analytical results showed that DFE is stable for all τ>0. On the other hand, there is a critical value of delay τ1>0, such that for all τ>τ1, the EEP is stable but unstable forτ<τ1. The critical value of delayτ1 is the bifurcation value where the HIV-1 in vivo dynamics undergoes a Hopf-bifurcation. This stability in both equilibria is achieved only if the drug efficacy 0≤ε≤1 is above a threshold value of ε_c. Numerical simulations show that this stability is achieved at the drug efficacy of εc=0.59 and time delay of τ1=0.65 days. This ratifies the fact that if CD4+T cells remain inactive for long periods of time τ>τ1 the HIV-1 viral materials will not be reproduced, and the immune system together with treatment will have enough time to clear the viral materials in the blood and thus the EEP is maintain.
Abstract: Mathematical models to describe in vivo and in vitro immunological response to infection in humans by HIV-1 have been of major concern due to the rich variety of parameters affecting its dynamics. In this paper, HIV-1 in vivo dynamics is studied to predict and describe its evolutions in presence of ARVs using delay differential equations. The delay...
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