Testing for Linearity of the Nonparametric Component of a Semiparametric Generalized Linear Model

• Activity Number: 35
• Type: Contributed
• Date/Time: Sunday, August 1, 2010 : 2:00 PM to 3:50 PM
• Sponsor: Section on Nonparametric Statistics
• Author(s): Chin-Shang Li*+
• Companies: University of California, Davis
• Keywords: B-spline ; Generalized linear model ; Generalized partially linear model ; Penalized log-likelihood ratio test ; Semiparametric generalized linear model

Abstract

A linear combination of fixed-knot cubic B-splines is used to model the nonparametric component of a semi-parametric generalized linear model. A penalized log-likelihood ratio test is proposed for the null hypothesis of the linearity of the nonparametric function. When the number of knots is fixed, the limiting null distribution of the penalized log-likelihood ratio test statistic is shown to be the distribution of a linear combination of independent chi-squared random variables, each with one degree of freedom. The smoothing parameter is selected that gives a specified value equal to the asymptotically expected value of the test statistic under the null hypothesis. A simulation study is conducted to study finite-sample performance of the test. The practicality of the proposed methodology is illustrated with a real-life data set.