Estimation and Testing on Independent Not Identically Distributed Observations Based on Rényi’s Pseudodistances

Impacto

Downloads

Downloads per month over past year



Castilla, Elena and Jaenada Malagón, María and Pardo Llorente, Leandro (2022) Estimation and Testing on Independent Not Identically Distributed Observations Based on Rényi’s Pseudodistances. IEEE transactions on information theory, 68 (7). pp. 4588-4609. ISSN 0018-9448

[thumbnail of pardo_estimation.pdf]
Preview
PDF
740kB

Official URL: https://ieeexplore.ieee.org/document/9732462



Abstract

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) with non-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 us 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 with non-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.


Item Type:Article
Uncontrolled Keywords:Asymptotic normality; Consistency; Independent not identically distributed observations; Influence function; minimum Rényi's pseudodistance estimators, Robustness; Wald-type tests.
Subjects:Sciences > Mathematics > Mathematical statistics
ID Code:74716
Deposited On:23 Sep 2022 08:09
Last Modified:23 Sep 2022 11:14

Origin of downloads

Repository Staff Only: item control page