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Abstract:
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Regression analysis focuses, unsurprisingly, on the regression function. However, estimators of the error distribution function are also useful, e.g. for tests about parametric models of the regression function. Most research on estimating error distribution functions is concerned with cases where the regression function is parametric, i.e. it depends on a finite-dimensional parameter, which can be estimated at the rate root-n. But if this function has nonparametric parts, possibly involving more than one covariate, different arguments are needed to obtain a stochastic expansion (and hence the root-n rate and asymptotic normality for the residual-based empirical distribution function). We discuss such approaches, based on suitable smoothing techniques, for various semiparametric additive regression models. Parametric and nonparametric regression functions are covered as special cases.
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