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

DOI

10.2991/jsta.2016.15.1.8How to use a DOI?

Keywords

Parametric maximum likelihood estimator; Independent non-identically distributed observations; Consistency; Asymptotic normality; Truncated data.

Abstract

We investigate the parametric maximum likelihood estimator for truncated data when the truncation value is different according to the observed individual or item. We extend Lehmann’s proof (1983) of the asymptotic properties of the parametric maximum likelihood estimator in the case of independent nonidentically distributed observations. Two cases are considered: either the number of distinct probability distribution functions that can be observed in the population from which the sample comes from is finite or this number is infinite. Sufficient conditions for consistency and asymptotic normality are provided for both cases.

Copyright

© 2017, the Authors. Published by Atlantis Press.

Open Access

This is an open access article distributed under the CC BY-NC license (http://creativecommons.org/licenses/by-nc/4.0/).

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TY  - JOUR
AU  - Fanny Leroy
AU  - Jean-Yves Dauxois
AU  - Pascale Tubert-Bitter
PY  - 2016
DA  - 2016/03/01
TI  - On the Parametric Maximum Likelihood Estimator for Independent but Non-identically Distributed Observations with Application to Truncated Data
JO  - Journal of Statistical Theory and Applications
SP  - 96
EP  - 107
VL  - 15
IS  - 1
SN  - 2214-1766
UR  - https://doi.org/10.2991/jsta.2016.15.1.8
DO  - 10.2991/jsta.2016.15.1.8
ID  - Leroy2016
ER  -