Open Access
February 1996 Quasi-likelihood models and optimal inference
Wolfgang Wefelmeyer
Ann. Statist. 24(1): 405-422 (February 1996). DOI: 10.1214/aos/1033066217


Consider an ergodic Markov chain on the real line, with parametric models for the conditional mean and variance of the transition distribution. Such a setting is an instance of a quasi-likelihood model. The customary estimator for the parameter is the maximum quasi-likelihood estimator. It is not efficient, but as good as the best estimator that ignores the parametric model for the conditional variance. We construct two efficient estimators. One is a convex combination of solutions of two estimating equations, the other a weighted nonlinear one-step least squares estimator, with weights involving predictors for the third and fourth centered conditional moments of the transition distribution. Additional restrictions on the model can lead to further improvement. We illustrate this with an autoregressive model whose error variance is related to the autoregression parameter.


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Wolfgang Wefelmeyer. "Quasi-likelihood models and optimal inference." Ann. Statist. 24 (1) 405 - 422, February 1996.


Published: February 1996
First available in Project Euclid: 26 September 2002

zbMATH: 0853.62066
MathSciNet: MR1389898
Digital Object Identifier: 10.1214/aos/1033066217

Primary: 62G20
Secondary: 62M05

Keywords: Autoregression , Efficient estimator , Markov chain , quasi-likelihood , weighted nonlinear least squares

Rights: Copyright © 1996 Institute of Mathematical Statistics

Vol.24 • No. 1 • February 1996
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