Verification of the Variance Structure in Quasi-likelihood Functions

• Activity Number: 22
• Type: Contributed
• Date/Time: Sunday, August 8, 2004 : 2:00 PM to 3:50 PM
• Sponsor: IMS
• Author(s): Steven G. Bai*+
• Companies: Pennsylvania State University
• Keywords: quasi-likelihood ; squared integrable estimating equations ; method of moment ; minimization of asymptotic variance

Abstract

The main purpose of this paper is to develop a method for verifying the validity of the variance assumption in a quasi-likelihood. The theoretical statisticians of all persuasions agree in the importance of the role played by the likelihood function in statistical inference. To obtain such likelihood it is necessary to have a probabilistic mechanism for the response. However, the inferences can be hard to draw from experiments in which there is insufficient information to construct a likelihood function. When such situations occur, a quasi-likelihood can be defined based only on the first two moments of the distribution. To use the quasi-likelihood effectively, however, we need to verify our assumptions on these moments. This paper is focused on the verification of the second moment. We assumed that the variance function is in the family of \mathcal{V} = \{ V(\alpha): \ \alpha \in \mathbb{R} \}.