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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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