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Quasi-likelihood estimation in semiparametric models. (English) Zbl 0798.62046
Summary: Suppose the expected value of a response variable \(Y\) may be written \(h({\mathbf X} \beta + \gamma ({\mathbf T}))\) where \({\mathbf X}\) and \({\mathbf T}\) are covariates, each of which may be vector-valued, \(\beta\) is an unknown parameter vector, \(\gamma\) is an unknown smooth function, and \(h\) is a known function. We outline a method for estimating the parameter \(\beta\), \(\gamma\) of this type of semiparametric model, using a quasi-likelihood function. Algorithms for computing the estimates are given and the asymptotic distribution theory for the estimators is developed. The generalization of this approach to the case in which \(Y\) is a multivariate response is also considered. The methodology is illustrated on two data sets and the results of a small Monte Carlo study are presented.

MSC:
62G05 Nonparametric estimation
62G07 Density estimation
62J12 Generalized linear models (logistic models)
62E20 Asymptotic distribution theory in statistics
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