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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.

##### MSC:
 62G07 Density estimation 62G20 Asymptotic properties of nonparametric inference