Abstract
In order to overcome the well-known multicollinearity problem, we propose a new Stochastic Restricted Liu Estimator in logistic regression model. In the mean square error matrix sense, the new estimation is compared with the Maximum Likelihood Estimation, Liu Estimator Stochastic Restricted Maximum Likelihood Estimator etc. Finally, a numerical example and a Monte Carlo simulation are given to explain some of the theoretical results.
Highlights
Consider the following multiple logistic regression model is yi =πi + εi,i =1, n, (1.1)which follows Bernoulli distribution with parameter πi as πi =exp( xi′β ) 1+ exp( xi′β ), (1.2)where β is a ( p +1) ×1 vector of coefficients and xi is the ith row of X, which is an n × ( p +1) data matrix with P explanatory variables, εi is independent with mean zero and variance πi (1− πi ) of the response yi
In order to overcome the well-known multicollinearity problem, we propose a new Stochastic Restricted Liu Estimator in logistic regression model
In the mean square error matrix sense, the new estimation is compared with the Maximum Likelihood Estimation, Liu Estimator Stochastic Restricted Maximum Likelihood Estimator etc
Summary
College of Mathematics and Statistics, North China University of Water Resources and Electric Power, Zhengzhou, China. Received: November 28, 2017 Accepted: January 29, 2018 Published: February 1, 2018
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