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Semiparametric estimation of quasi-score. (Estimation semi-paramétrique de quasi-score.) (French) Zbl 0912.62046
Summary: The method of maximum quasi-likelihood estimation gives satisfactory results in a parametric regression model, where the link function \(r\) and the variance function \(V\) are well specified. In semiparametric models, when the functions \(r\) and \(V\) are unknown, this method fails. Nevertheless, it is possible to define the quasi-score function and its estimation, computed from kernel regression estimators of the functions \(r\) and \(V\). We propose an estimator for the regression coefficients based on a one step Newton-Raphson iteration in a maximum quasi-likelihood optimization starting from an initial \(\sqrt n\)-consistent estimate and using the estimated quasi score. We derive the asymptotic properties of this estimator and its semi parametric efficiency.

62G07 Density estimation
62G20 Asymptotic properties of nonparametric inference