Abstract
In order to overcome multicollinearity, we propose a stochastic restricted Liu-type maximum likelihood estimator by incorporating Liu-type maximum likelihood estimator to the logistic regression model when the linear restrictions are stochastic. We also discuss the properties of the new estimator. Moreover, we give a method to choose the biasing parameter in the new estimator. Finally, a simulation study is given to show the performance of the new estimator.
Highlights
Consider the following logistic regression model yi = i + "i; i = 1; : : : ; n; (1) where i = (xi) = E [yi] exi 1+exi, yi Bernoulli ( i) and 0; 1; : : : ;> p denotes the unknown (p+1)-vector of regression coe¢ cients, X = (x1; : : : ; xn)> is the n (p + 1) data matrix with xi = (1; x1i; : : : ; xpi)> and "i’s are independent with zero mean and their variance equal to wi = i (1 i).In the estimation process of the coe¢ cient vector, one often uses the maximum likelihood (ML) approach
By combining the Liu-type maximum likelihood estimator ([11]) and stochastic linear restrictions, we propose a new estimator called stochastic restricted Liu-type maximum likelihood estimator to overcome multicollinearity
Incorporating the LTE to the logistic regression model under the stochastic linear restriction, we propose a new biased estimator which is called stochastic restricted Liu-type maximum likelihood estimator (SRLTE)
Summary
We suppose that is subjected to lie in the sub-space restriction H = h, where H is q (p + 1) known matrix and h is a q 1 vector of pre-speci...ed values. This problem was studied in [7], [6], [15], [16]. We will discuss the logistic regression model with stochastic linear restrictions. By combining the Liu-type maximum likelihood estimator ([11]) and stochastic linear restrictions, we propose a new estimator called stochastic restricted Liu-type maximum likelihood estimator to overcome multicollinearity.
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