Uniform in bandwidth exact rates for a class of kernel estimators

Mathematics – Statistics Theory

Scientific paper

Rate now

  [ 0.00 ] – not rated yet Voters 0   Comments 0

Details

Published in the Annals of the Institute of Statistical Mathematics Volume 63, p. 1077-1102 (2011)

Scientific paper

Given an i.i.d sample $(Y_i,Z_i)$, taking values in $\RRR^{d'}\times \RRR^d$, we consider a collection Nadarya-Watson kernel estimators of the conditional expectations $\EEE(+d_g(z)\mid Z=z)$, where $z$ belongs to a compact set $H\subset \RRR^d$, $g$ a Borel function on $\RRR^{d'}$ and $c_g(\cdot),d_g(\cdot)$ are continuous functions on $\RRR^d$. Given two bandwidth sequences $h_n<\wth_n$ fulfilling mild conditions, we obtain an exact and explicit almost sure limit bounds for the deviations of these estimators around their expectations, uniformly in $g\in\GG,\;z\in H$ and $h_n\le h\le \wth_n$ under mild conditions on the density $f_Z$, the class $\GG$, the kernel $K$ and the functions $c_g(\cdot),d_g(\cdot)$. We apply this result to prove that smoothed empirical likelihood can be used to build confidence intervals for conditional probabilities $\PPP(Y\in C\mid Z=z)$, that hold uniformly in $z\in H,\; C\in \CC,\; h\in [h_n,\wth_n]$. Here $\CC$ is a Vapnik-Chervonenkis class of sets.

No associations

LandOfFree

Say what you really think

Search LandOfFree.com for scientists and scientific papers. Rate them and share your experience with other people.

Rating

Uniform in bandwidth exact rates for a class of kernel estimators does not yet have a rating. At this time, there are no reviews or comments for this scientific paper.

If you have personal experience with Uniform in bandwidth exact rates for a class of kernel estimators, we encourage you to share that experience with our LandOfFree.com community. Your opinion is very important and Uniform in bandwidth exact rates for a class of kernel estimators will most certainly appreciate the feedback.

Rate now

     

Profile ID: LFWR-SCP-O-445603

  Search
All data on this website is collected from public sources. Our data reflects the most accurate information available at the time of publication.