Exact norms of a Stein-type operator and associated stochastic orderings

Exact norms of a Stein-type operator and associated stochastic orderings

Motivated by asymptotic expansions in the central limit theorem, we find exact norms of a sequence of Stein-type operators. The proof is based on new stochastic comparisons in distribution between the difference of two independent transformed normal variables and the standard normal distribution.

Gespeichert in:
Bibliographische Detailangaben
Veröffentlicht in:Probability theory and related fields 2003-11, Vol.127 (3), p.353-366
Hauptverfasser: LEFEVRE, Claude, UTEV, Sergey
Format: Artikel
Sprache:eng
Schlagworte:
Asymptotic series
Central limit theorem
Digital Object Identifier
Distribution theory
Exact sciences and technology
Independent variables
Limit theorems
Mathematical analysis
Mathematics
Normal distribution
Norms
Operator theory
Polynomials
Probability
Probability and statistics
Probability theory and stochastic processes
Random variables
Sciences and techniques of general use
Online-Zugang:Volltext
Tags: Tag hinzufügen
Keine Tags, Fügen Sie den ersten Tag hinzu!
Beschreibung
Zusammenfassung:Motivated by asymptotic expansions in the central limit theorem, we find exact norms of a sequence of Stein-type operators. The proof is based on new stochastic comparisons in distribution between the difference of two independent transformed normal variables and the standard normal distribution.
ISSN:0178-8051
1432-2064
DOI:10.1007/s00440-003-0288-9