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Estimating the conditional error distribution in non-parametric regression. (English) Zbl 1246.62107

Summary: We consider a general nonparametric regression model, where the distribution of the error, given the covariate, is modelled by a conditional distribution function. For the estimation, a kernel approach as well as the (kernel based) empirical likelihood method are discussed. The latter method allows for incorporation of additional information on the error distribution into the estimation. We show weak convergence of the corresponding empirical processes to Gaussian processes and compare both approaches in asymptotic theory and by means of a simulation study.

MSC:

62G08 Nonparametric regression and quantile regression
62G05 Nonparametric estimation
62G30 Order statistics; empirical distribution functions
62G20 Asymptotic properties of nonparametric inference
65C60 Computational problems in statistics (MSC2010)
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