On the parametric maximum likelihood estimator for independent but non-identically distributed observations with application to truncated data

Fanny Leroy (1) , Jean-Yves Dauxois (2) , Pascale Tubert-Bitter (1)

1 CESP - Centre de recherche en épidémiologie et santé des populations
2 IMT - Institut de Mathématiques de Toulouse UMR5219

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 non-identically 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.

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

Domaines: Applications [stat.AP]; Théorie [stat.TH]

Fanny Leroy, Jean-Yves Dauxois, Pascale Tubert-Bitter. On the parametric maximum likelihood estimator for independent but non-identically distributed observations with application to truncated data. Journal of Statistical Theory and Applications, 2016, vol. 15 (1), pp.96 - 107. ⟨10.2991/jsta.2016.15.1.8⟩. ⟨hal-00865962⟩