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The Semiparametric Normal Variance‐Mean Mixture Model
Author(s) -
Korsholm Lars
Publication year - 2000
Publication title -
scandinavian journal of statistics
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 1.359
H-Index - 65
eISSN - 1467-9469
pISSN - 0303-6898
DOI - 10.1111/1467-9469.00187
Subject(s) - mathematics , estimator , semiparametric model , asymptotic distribution , semiparametric regression , consistency (knowledge bases) , parametric statistics , delta method , statistics , consistent estimator , normal distribution , econometrics , minimum variance unbiased estimator , discrete mathematics
We study the normal variance‐mean mixture model from a semiparametric point of view, i.e. we let the mixing distribution belong to a non‐parametric family. The main results are consistency of the non‐parametric maximum likelihood estimator and construction of an asymptotically normal and efficient estimator for the Euclidian part of the parameter. We study the model according to the theory outlined in the monograph by Bickel et al. (1993) and apply a general result (based on the theory of empirical processes) for semiparametric models from van der Vaart (1996) to prove asymptotic normality and efficiency of the proposed estimator.