Statistical inference for conditional curves: Poisson process approach (Q1193350)

The aim of this paper is to present a unified treatment of conditional statistical problems, to some extent. On the basis of an approximation of a truncated, empirical point process by a suitable Poisson point process with the same intensity measure the investigation of asymptotic properties of estimates of functionals of the conditional distribution function is reduced to the study of a corresponding unconditional problem. The approximation error is characterized by bounds of the Hellinger distance between the distributions of the considered processes. This new method of statistical inference for conditional curves is exemplified by the proof of the asymptotic normality of well-known nonparametric estimates of regression, conditional quantiles, the conditional distribution function itself and conditional \(V\)-statistics. Finally, the projection pursuit technique is indicated in another example.