Semiparametric Estimation of the Center of an Unknown Symmetric Population Under Selection Bias

• Activity Number: 238
• Type: Contributed
• Date/Time: Monday, July 30, 2012 : 2:00 PM to 3:50 PM
• Sponsor: Section on Nonparametric Statistics
• Author(s): Mi Jeong Kim*+ and Marc Genton and Yanyuan Ma
• Companies: Texas A&M University and Texas A&M University and Texas A&M University
• Keywords: Robustness ; Selection Bias ; Semiparametric Model ; Skewness ; Symmetric Distribution

Abstract

We study a class of semi parametric skewed distributions arising when the sample selection process causes sampling bias for the observations. Based on semi parametric 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 center 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 a real data example of ambulatory expenditures to illustrate the applicability of the methods in practice.