On the Parametric Maximum Likelihood Estimator for Independent but Non-identically Distributed Observations with Application to Truncated Data

Leroy, Fanny; Dauxois, Jean-Yves; Tubert-Bitter, Pascale

doi:10.2991/jsta.2016.15.1.8

Cited by 6 publications

(1 citation statement)

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“…The proof follows similar steps that the proof presented in [12] for the minimum DPD estimators for i.n.i.d.o and the proof presented in [17] for the MLE with i.n.i.d.o.…”

Section: A Proof Of Resultsmentioning

confidence: 77%

Estimation and testing on independent not identically distributed observations based on Rényi's pseudodistances

Castilla¹,

Jaenada²,

Pardo³

2021

Preprint

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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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“…The proof follows similar steps that the proof presented in [12] for the minimum DPD estimators for i.n.i.d.o and the proof presented in [17] for the MLE with i.n.i.d.o.…”

Section: A Proof Of Resultsmentioning

confidence: 77%