Set-indexed conditional empirical and quantile processes based on dependent data

Qiwei Yao and Wolfgang Polonik

LSE Research Online Documents on Economics from London School of Economics and Political Science, LSE Library

Abstract: We consider a conditional empirical distribution of the form Fn(C ∣ x)=∑nt=1 ωn(Xt−x) I{Yt∈C} indexed by C∈ ℓ, where {(Xt, Yt), t=1, …, n} are observations from a strictly stationary and strong mixing stochastic process, {ωn(Xt−x)} are kernel weights, and ℓ is a class of sets. Under the assumption on the richness of the index class ℓ in terms of metric entropy with bracketing, we have established uniform convergence and asymptotic normality for Fn(· ∣ x). The key result specifies rates of convergences for the modulus of continuity of the conditional empirical process. The results are then applied to derive Bahadur–Kiefer type approximations for a generalized conditional quantile process which, in the case with independent observations, generalizes and improves earlier results. Potential applications in the areas of estimating level sets and testing for unimodality (or multimodality) of conditional distributions are discussed.

Keywords: Bahadur–Kiefer approximation; conditional distribution; covering number; empirical process theory; generalized conditional quantile; level set; minimum volume predictor; Nadaraya–Watson regression estimator; nonlinear time series; strong mixing (search for similar items in EconPapers)
JEL-codes: C1 (search for similar items in EconPapers)
Date: 2002-02
References: Add references at CitEc
Citations: View citations in EconPapers (5)

Published in Journal of Multivariate Analysis, February, 2002, 80(2), pp. 234-255. ISSN: 0047-259X

Downloads: (external link)
http://eprints.lse.ac.uk/5878/ Open access version. (application/pdf)

Related works:
This item may be available elsewhere in EconPapers: Search for items with the same title.

Export reference: BibTeX RIS (EndNote, ProCite, RefMan) HTML/Text

Persistent link: https://EconPapers.repec.org/RePEc:ehl:lserod:5878

Access Statistics for this paper

More papers in LSE Research Online Documents on Economics from London School of Economics and Political Science, LSE Library LSE Library Portugal Street London, WC2A 2HD, U.K.. Contact information at EDIRC.
Bibliographic data for series maintained by LSERO Manager ().