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首页> 美国政府科技报告 >Small Sample Properties of Norm-Restricted Maximum Likelihood Estimators for Logistic Regression Models
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Small Sample Properties of Norm-Restricted Maximum Likelihood Estimators for Logistic Regression Models

机译：Logistic回归模型范数约束极大似然估计的小样本性质

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This paper develops alternatives to maximum likelihood estimators (MLE) for logistic regression models and compares the mean squared error (MSE) of the estimators. The MLE for the vector underlying success probabilities has low MSE only when the true probabilities are extreme (i.e., near 0 or 1). Extreme probabilities correspond to logistic regression parameter vectors which are large in norm. A competing 'restricted' MLE and an empirical version of it are suggested as estimators with better performance than the MLE for central probabilities. An approximate EM-algorithm for estimating the restriction is described. As in the case of normal theory ridge estimators, the proposed estimators are shown to be formally derivable by Bayes and empirical Bayes arguments. Binary response models; EM algorithm; Empirical Bayes method; Logistic regression; Posterior modes; Restricted maximum; Likelihood; Ridge regression. (jes)

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