B. M. Golam Kibria

Bio: B. M. Golam Kibria is an academic researcher from Florida International University. The author has contributed to research in topics: Estimator & Multicollinearity. The author has an hindex of 25, co-authored 143 publications receiving 2532 citations. Previous affiliations of B. M. Golam Kibria include Carleton University & University of Western Ontario.

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

Abstract: 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.

Performance of some new preliminary test ridge regression estimators and their properties

Abstract: The problem of estimation of the regression coefficients in a multiple regression model is considered under multicollinearity situation when it is suspected that the regression coefficients may be restricted to a subspace. We present the estimators of the regression coefficients combining the idea of preliminary test and ridge regression methodology. Accordingly, we consider three estimators, namely, the unrestricted ridge regression estimator (URRE), the restricted ridge regression estimator (RRRE), and finally, the preliminary test ridge regression estimator (PTRRE). The biases, variancematrices and mean square errors (mse) of the estimators are derived and compared with the usual estimators. Regions of optimality of the estimators are determined by studying the mse criterion. The conditions of superiority of the estimators over the traditional estimators as in Saleh and Han (1990) and Ali and Saleh (1991) have also been discussed.

A New Ridge-Type Estimator for the Linear Regression Model: Simulations and Applications

Abstract: The ridge regression-type (Hoerl and Kennard, 1970) and Liu-type (Liu, 1993) estimators are consistently attractive shrinkage methods to reduce the effects of multicollinearity for both linear and nonlinear regression models. This paper proposes a new estimator to solve the multicollinearity problem for the linear regression model. Theory and simulation results show that, under some conditions, it performs better than both Liu and ridge regression estimators in the smaller MSE sense. Two real-life (chemical and economic) data are analyzed to illustrate the findings of the paper.

The Design and Analysis of Experiments

Abstract: THE DESIGN AND ANALYSIS OF EXPERIMENTS. By Oscar Kempthorne. New York, John Wiley and Sons, Inc., 1952. 631 pp. $8.50. This book by a teacher of statistics (as well as a consultant for \"experimenters\") is a comprehensive study of the philosophical background for the statistical design of experiment. It is necessary to have some facility with algebraic notation and manipulation to be able to use the volume intelligently. The problems are presented from the theoretical point of view, without such practical examples as would be helpful for those not acquainted with mathematics. The mathematical justification for the techniques is given. As a somewhat advanced treatment of the design and analysis of experiments, this volume will be interesting and helpful for many who approach statistics theoretically as well as practically. With emphasis on the \"why,\" and with description given broadly, the author relates the subject matter to the general theory of statistics and to the general problem of experimental inference. MARGARET J. ROBERTSON

Table Of Integrals Series And Products

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