title: Semiparametric location estimation under non-random sampling.
abstract: 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.
authors.affiliation: Department of Statistics, Texas A&M University, College Station, TX 77843-3143, USA.
authors.forename: Marc G
authors.initials: MG
authors.lastname: Genton
authors.affiliation: Department of Statistics, Texas A&M University, College Station, TX 77843-3143, USA.
authors.forename: Mijeong
authors.initials: M
authors.lastname: Kim
authors.affiliation: Department of Statistics, Texas A&M University, College Station, TX 77843-3143, USA.
authors.forename: Yanyuan
authors.initials: Y
authors.lastname: Ma
keywords: robustness; selection bias; semiparametric model; skew-symmetric distribution; skewness