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M ‐estimation Under a Two‐Sample Semiparametric Model
Author(s) -
Zhang Biao
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 - 10.1111/1467-9469.00188
Subject(s) - estimator , mathematics , semiparametric model , semiparametric regression , statistics , parametric statistics , parametric model , sample (material) , econometrics , chemistry , chromatography
We consider M ‐estimation under a two‐sample semiparametric model in which the log ratio of two unknown density functions has a known parametric form. This two‐sample semiparametric model, arising naturally from case‐control studies and logistic discriminant analysis, can be regarded as a biased sampling model. A new class of M ‐estimators are constructed on the basis of the maximum semiparametric likelihood estimator of the underlying distribution function. It is shown that the proposed M ‐estimators are consistent and asymptotically normally distributed. A simulation study is presented to demonstrate the performance of the proposed M ‐estimators.