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A generalized semiparametric regression and its efficient estimation
Author(s) -
Lin Lu,
Liu Lili,
Cui Xia,
Wang Kangning
Publication year - 2021
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/sjos.12430
Subject(s) - semiparametric regression , mathematics , estimator , semiparametric model , nonparametric statistics , function (biology) , measure (data warehouse) , likelihood function , estimating equations , exponential family , score , statistics , regression analysis , econometrics , estimation theory , computer science , data mining , biology , evolutionary biology
We investigate a generalized semiparametric regression. Such a model can avoid the risk of wrongly choosing the base measure function. We propose a profile likelihood to efficiently estimate both parameter and nonparametric function. The main difference from the classical profile likelihood is that the profile likelihood proposed is a functional of the base measure function, instead of a function of a real variable. By making the most of the structure information of the semiparametric exponential family, we get an explicit expression of the estimator of the least favorable curve. It ensures that the new profile likelihood is computationally simple. Due to the use of the least favorable curve, the semiparametric efficiency is achieved successfully and the estimation bias is reduced significantly. Simulation studies can illustrate that our proposal is much better than the existing methodologies for most cases under study, and is robust to the different model conditions.