On nonparametric regression for IID observations in a general setting

Efromovich, Sam

Ann. Statist., Tome 24 (1996) no. 6, p. 1126-1144 / Harvested from Project Euclid

Résumé

We consider the problem of sharp-optimal estimation of a response function $f(x)$ in a random design nonparametric regression under a general model where a pair of observations $(Y, X)$ has a joint density $p(y, x) = p(y|f(x)) \pi(x)$. We wish to estimate the response function with optimal minimax mean integrated squared error convergence as the sample size tends to $\infty$. Traditional regularity assumptions on the conditional density $p(y| \theta)$ assumed for parameter $\theta$ estimation are sufficient for sharp-optimal nonparametric risk convergence as well as for the existence of the best constant and rate of risk convergence. This best constant is a nonparametric analog of Fisher information. Many examples are sketched including location and scale families, censored data, mixture models and some well-known applied examples. A sequential approach and some aspects of experimental design are considered as well.

Détail

Publié le : 1996-06-14
Classification:  Nonparametric regression,  curves estimation,  sharp-optimal risk convergence,  sequential estimation,  location and scale families,  censored data,  mixtures,  62G05,  62G20,  62J02,  62E20,  62F35