轮廓似然函数及其应用

Profile Likelihood and its Application

目的介绍轮廓似然方法及其两个应用。方法拟合logistic回归模型,计算轮廓似然的置信区间,并与Wald置信区间进行比较;采用轮廓似然方法解决多余参数过多的模型拟合问题。结果轮廓似然可以解决偏态分布下Wald置信区间失效的问题;最大轮廓似然估计与最大似然估计的结果是一致的,而轮廓似然仅需要较弱的假设条件。结论参数呈非正态分布时,轮廓似然置信区间要优于Wald置信区间;轮廓似然作为最大似然估计的替代方法,可以解决最大似然无法计算或计算困难的问题,也可以提高模型的适用性。

Objective To introduce the method and applica- tion of profile likelihood. Methods Comparing the confidence interval of profile likelihood with that of Wald under the logistic model. Using profile likelihood to fit models with overmany parameters. Results Confidence interval of profile likelihood can solve the problem that confidence interval of Wald fails. The maximum profile likelihood estimator is equivalent to the maximum likelihood estimator with a weaker assumption. Conclusion Profile likelihood confidence interval is superior to Wald confidence interval for the parameter from a skewed distribution; Profile likelihood estimator can be worked out when the MLE is hardly computed, so that the applica- bility is increased.