Asymptotic properties of kernel density estimators when applying importance sampling

Research output: Chapter in Book/Report/Conference proceedingConference contribution

4 Scopus citations

Abstract

We study asymptotic properties of kernel estimators of an unknown density when applying importance sampling (IS). In particular, we provide conditions under which the estimators are consistent, both pointwise and uniformly, and are asymptotically normal. We also study the optimal bandwidth for minimizing the asymptotic mean square error (MSE) at a single point and the asymptotic mean integrated square error (MISE). We show that IS can improve the asymptotic MSE at a single point, but IS always increases the asymptotic MISE. We also give conditions ensuring the consistency of an IS kernel estimator of the sparsity function, which is the inverse of the density evaluated at a quantile. This is useful for constructing a confidence interval for a quantile when applying IS. We also provide conditions under which the IS kernel estimator of the sparsity function is asymptotically normal. We provide some empirical results from experiments with a small model.

Original languageEnglish (US)
Title of host publicationProceedings of the 2011 Winter Simulation Conference, WSC 2011
Pages556-568
Number of pages13
DOIs
StatePublished - 2011
Event2011 Winter Simulation Conference, WSC 2011 - Phoenix, AZ, United States
Duration: Dec 11 2011Dec 14 2011

Publication series

NameProceedings - Winter Simulation Conference
ISSN (Print)0891-7736

Other

Other2011 Winter Simulation Conference, WSC 2011
CountryUnited States
CityPhoenix, AZ
Period12/11/1112/14/11

All Science Journal Classification (ASJC) codes

  • Software
  • Modeling and Simulation
  • Computer Science Applications

Fingerprint Dive into the research topics of 'Asymptotic properties of kernel density estimators when applying importance sampling'. Together they form a unique fingerprint.

Cite this