Sieve Maximum Likelihood Estimation Using B-Spline Smoothing in the Generalized Linear Models with an Unknown Link Function

• Activity Number: 30
• Type: Contributed
• Date/Time: Sunday, August 9, 2015 : 2:00 PM to 3:50 PM
• Sponsor: Government Statistics Section
• Author(s): Mengdie Yuan*
• Companies: FDA
• Keywords: Semiparametric Modeling ; B-spline Smoothing ; Sieve Maximum Likelihood Estimation ; Generalized Linear Models ; Unknown Link Function

Abstract

In standard generalized linear mixed models, the link functions relating the linear predictor and the mean of the distribution are assumed to be known. Mis-specification of the link functions may lead to biased estimators of the regression parameters as well as the variance parameters for the random effects. In this paper, we study the generalized linear mixed models with an unknown link function. Specifically, we propose sieve maximum likelihood estimation procedures by using B-splines, and establish the consistency and asymptotic normality of the proposed sieve maximum likelihood estimators. Extensive simulation studies along with an application to an epileptic study are provided to evaluate the finite-sample performance of the proposed methods.