基于Rényi伪距离的独立异分布观测值的估计与检验
Estimation and testing on independent not identically distributed observations based on Rényi's pseudodistances
摘要：
在现实生活中，我们经常处理独立但不相同分布的观测（i.n.i.d.o），其中最着名的统计模型是没有随机协变量的多元线性回归模型（MLRM）。虽然经典的方法是基于最大似然估计（MLE），它是众所周知的缺乏鲁棒性的小偏差从假设条件。本文基于Rényi伪距离（RP），在已知未知参数信息的情况下，引入了一类新的估计量.这个估计族，比如说最小RP估计（因为它们是通过最小化数据的假设分布和经验分布之间的RP获得的），包含MLE作为特殊情况，并且可以应用于没有随机协变量的MLRM。基于这些估计量，我们引入Wald型检验来检验简单和复合的零假设，作为经典的基于极大似然估计的Wald检验的扩展。给出了估计量的影响函数和Wald型检验，并进行了分析。最后，为了评估所提出的方法的性能和一些现实生活中的数据进行了分析说明的目的，开发了一个模拟研究。
英文摘要：
In real life we often deal with independent but not identically distributed observations (i.n.i.d.o), for which the most well-known statistical model is the multiple linear regression model (MLRM) without random covariates. While the classical methods are based on the maximum likelihood estimator (MLE), it is well known its lack of robustness to small deviations from the assumed conditions. In this paper, and based on the Rényi's pseudodistance (RP), we introduce a new family of estimators in case our information about the unknown parameter is given for i.n.i.d.o.. This family of estimators, let say minimum RP estimators (as they are obtained by minimizing the RP between the assumed distribution and the empirical distribution of the data), contains the MLE as a particular case and can be applied, among others, to the MLRM without random covariates. Based on these estimators, we introduce Wald-type tests for testing simple and composite null hypotheses, as an extension of the classical MLE-based Wald test. Influence functions for the estimators and Wald-type tests are also obtained and analysed. Finally, a simulation study is developed in order to asses the performance of the proposed methods and some real-life data are analysed for illustrative purpose.
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