B. M. Golam Kibria

Performance of Some New Ridge Regression Estimators

Abstract In the ridge regression analysis, the estimation of ridge parameter k is an important problem. Many methods are available for estimating such a parameter. This article has considered some of these methods and also proposed some new estimators based on generalized ridge regression approach. A simulation study has been made to evaluate the performance of proposed estimators based on the minimum mean squared error (MSE) criterion. The simulation study indicates that under certain conditions the proposed estimators perform well compared to least squares estimators (LSE) and other popular existing estimators. Finally, a numerical example has been analyzed and its findings support the simulation results to some extent.

On Some Ridge Regression Estimators: An Empirical Comparisons

In ridge regression analysis, the estimation of the ridge parameter k is an important problem. Many methods are available for estimating such a parameter. This article reviewed and proposed some estimators based on Kibria (2003) and Khalaf and Shukur (2005). A simulation study has been made and mean squared error (MSE) criteria are used to compare the performances of the estimators. We observed that under certain conditions some of the proposed estimators performed well compared to the ordinary least squared (OLS) estimator and some existing popular estimators. Finally, a numerical example has been considered to illustrate the performance of the estimators.

Normal and Student's t Distributions and Their Applications

The most important properties of normal and Student t-distributions are presented. A number of applications of these properties are demonstrated. New related results dealing with the distributions of the sum, product and ratio of the independent normal and Student distributions are presented. The materials will be useful to the advanced undergraduate and graduate students and practitioners in the various fields of science and engineering.

Some Liu and ridge-type estimators and their properties under the ill-conditioned Gaussian linear regression model

The estimation of the regression parameters for the ill-conditioned Gaussian linear regression model are considered in this paper. Accordingly, we consider some improved Liu [A new class of biased estimate in linear regression, Commun. Stat. Theory Methods 22 (1993), pp. 393–402] type estimators, namely the unrestricted Liu estimator, restricted Liu estimator and the preliminary test Liu estimator (PTLE) for estimating the regression parameters. The performances of the proposed estimators are compared based on the quadratic bias and risk functions under both null and alternative hypotheses. The conditions of superiority of the proposed estimators for departure parameter, Δ, and biasing parameter, d, are given. We also numerically compared the performance of PTLE with the preliminary test ridge regression estimator (PTRRE) and concluded that for small values of d and ridge parameter k, PTLE performed better than the PTRRE; otherwise the PTRRE performed better than PTLE in the sense of smaller MSE.

Testing and evaluating virus detectors for handheld devices

The widespread use of personal digital assistants and smartphones gives securing these devices a high priority. Yet little attention has been placed on protecting handheld devices against viruses. Currently available antivirus software for handhelds is few in number. At this stage, the opportunity exists for the evaluation and improvement of current solutions. By pinpointing weaknesses in the current antivirus software, improvements can be made to properly protect these devices from a future tidal wave of viruses. This research evaluates four currently available antivirus solutions for handheld devices. A formal model of virus transformation that provides transformation traceability is presented. Two sets of ten tests each were administered; nine tests from each set involved the modification of source code of two known viruses for handheld devices. The testing techniques used are well established in PC testing; thus the focus of this research is solely on handheld devices. Statistical analysis of the test results show high false negative production rates for the antivirus software and an overall false negative production rate of 47.5% with a 95% confidence interval between 36.6% and 58.4%. This high rate shows that current solutions poorly identify modified versions of a virus. The virus is left undetected and capable of spreading, infecting and causing damage.

A Simulation Study of Some Ridge Regression Estimators under Different Distributional Assumptions

Based on the work of Khalaf and Shukur (2005), Alkhamisi et al. (2006), and Muniz et al. (2010), this article considers several estimators for estimating the ridge parameter k. This article differs from aforementioned articles in three ways: (1) Data are generated from Normal, Students t, and F distributions with appropriate degrees of freedom; (2) The number of regressors considered are from 4–12 instead of 2–4, which are the usual practice; (3) Both mean square error (MSE) and prediction sum of square (PRESS) are considered as the performance criterion. A simulation study has been conducted to compare the performance of the estimators. Based on the simulation study we found that, increasing the correlation between the independent variables has negative effect on the MSE and PRESS. However, increasing the number of regressors has positive effect on MSE and PRESS. When the sample size increases the MSE decreases even when the correlation between the independent variables is large. It is interesting to note that the dominance pictures of the estimators are remained the same under both the MSE and PRESS criterion. However, the performance of the estimators depends on the choice of the assumption of the error distribution of the regression model.

Performance of the shrinkage preliminary test ridge regression estimators based on the conflicting of W, LR and LM tests

The shrinkage preliminary test ridge regression estimators (SPTRRE) based on the Wald (W), the likelihood ratio (LR) and the Lagrangian multiplier (LM) tests are considered in this paper. The bias and the risk functions of the proposed estimators are derived. The regions of optimality of the estimators are determined under the quadratic risk function. Under the null hypothesis, the SPTRRE based on LM test has the smallest risk, followed by the estimators based on LR and W tests. However, the SPTRRE based on W test performs the best followed by the LR and LM based estimators when the parameter moves away from the subspace of the restrictions. The conditions of superiority of the proposed estimator for both ridge and departure parameters are discussed. The optimum choice of the level of significance becomes the traditional choice by using the W test for all non-negative ridge parameters.

Optimum critical value for pre-test estimator

ABSTRACT We propose a preliminary test least squares estimator (PTLSE) based on a fixed critical value for the preliminary test (PT). We compare the performance of the proposed estimator with that of the Brook (1976) and Han and Bancroft (1968) criterion. Table and graphs of relative efficiencies are presented to support the view of using fixed critical value for the PT. It is observed that the proposed or Brooks method are conservative for fixed q, whereas that of Han and Bancroft is flexible. If the researchers are concern about the minimum guaranteed efficiency, they might select our or Brooks method. However, if they are willing to accept higher size of test and want to have higher minimum guaranteed efficiency, they should select the Han and Bancroft method.

Estimating the Population Coefficient of Variation by Confidence Intervals

Several researchers considered various interval estimators for estimating the population coefficient of variation (CV) of symmetric and skewed distributions. Since they considered at different times and under different simulation conditions, their performances are not comparable as a whole. In this article, an attempt has been made to review some existing estimators along with some proposed methods and compare them under the same simulation condition. In particular, we have considered Hendricks and Robey, Mckay, Miller, Sharma and Krishna, Curto and Pinto, and also some bootstrap proposed interval estimators for estimating the population CV. A simulation study has been conducted to compare the performance of the estimators. Both average widths and coverage probabilities are considered as a criterion of the good estimators. Two real life health related data sets are analyzed to illustrate the findings of the article. Based on the simulation study, some possible good interval estimators have been recommended for the practitioners.

On some confidence intervals for estimating the mean of a skewed population

A number of methods are available in the literature to measure confidence intervals. Here, confidence intervals for estimating the population mean of a skewed distribution are considered. This note proposes two alternative confidence intervals, namely, Median t and Mad t, which are simple adjustments to the Students t confidence interval. In order to compare the performance of these intervals, the following criteria are considered: (i) coverage probability; (ii) average width; and (iii) ratio of coverage to width. A simulation study has been undertaken to compare the performance of the intervals. The simulation study shows that for small sample size and moderate to highly skewed distributions, the proposed Median t performs the best in the sense of higher coverage, and the Mad t performs best in the sense of smaller confidence width. The proposed methods are very easy to calculate and are not overly computer-intensive, like Bootstrap confidence intervals. Some real-life examples have been considered that support the findings of the paper to some extent.