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Semiparametric location estimation under non‐random sampling
Author(s) -
Genton Marc G.,
Kim Mijeong,
Ma Yanyuan
Publication year - 2012
Publication title -
stat
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 0.61
H-Index - 18
ISSN - 2049-1573
DOI - 10.1002/sta4.2
Subject(s) - estimator , sample (material) , variance (accounting) , asymptotic distribution , population , mathematics , semiparametric model , statistics , sampling (signal processing) , econometrics , estimation , computer science , economics , chemistry , demography , accounting , management , filter (signal processing) , chromatography , sociology , computer vision
We study a class of semiparametric skewed distributions arising when the sample selection process produces non‐randomly sampled observations. Based on semiparametric theory and taking into account the symmetric nature of the population distribution, we propose both consistent estimators, i.e. robust to model mis‐specification, and efficient estimators, i.e. reaching the minimum possible estimation variance, of the location of the symmetric population. We demonstrate the theoretical properties of our estimators through asymptotic analysis and assess their finite sample performance through simulations. We also implement our methodology on a real data example of ambulatory expenditures to illustrate the applicability of the estimators in practice. Copyright © 2012 John Wiley & Sons, Ltd.