Limit theorems for trimmed sums
type: Item
instance of: scholarly article
title: Limit theorems for trimmed sums
zbMATH Open document ID: 0759.62018
DOI: 10.1007/BF01058722
author: Yuji Kasahara
author: M. Maejima
published in: Journal of Theoretical Probability
publication date: 1993-01-17T00:00:00Z
review text: For \(n\geq 1\), let \(X^{(n)}_ 1\leq\cdots\leq X^{(n)}_ n\) be the order statistics from the first \(n\) observations of an i.i.d. sequence with distribution function \(F\), whose left-continuous inverse is \(Q\). Let \(h\) be a measurable function such that \(h\circ Q\) is square-integrable, and define, for \(n\geq 1\), the stochastic process \[ X_ n(t)=n^{- 1/2}\left\{\sum^{[nt]}_{j=[na]+1} h(X^{(n)}_ j)-n \int^ t_ a h\circ Q(x)dx\right\}. \] The limiting process of \(\{X_ n(t)\}\) as \(n\to\infty\) is determined explicitly. A similar study of the weighted trimmed sums \(\left\{\sum^{[nt]}_{j=1} J(j/n)X^{(n)}_ j, n\geq 1\right\}\) is also presented.
Mathematics Subject Classification ID: 62G30
Mathematics Subject Classification ID: 60F05
Mathematics Subject Classification ID: 62G20
zbMATH DE Number: 96934
zbMATH Keywords: central limit theorem
zbMATH Keywords: heavily trimmed sums
zbMATH Keywords: Brownian bridge
zbMATH Keywords: smoothly trimmed sums
zbMATH Keywords: order statistics
zbMATH Keywords: left-continuous inverse
reviewed by: R. James Tomkins
MaRDI profile type: Publication
cites work: Q5560061
cites work: The asymptotic distribution of trimmed sums
cites work: Q1099492
cites work: Random means
cites work: Q3395931
cites work: The asymptotic distribution of the trimmed mean
full work available at URL: https://doi.org/10.1007/bf01058722
OpenAlex ID: W2058221720
description: scientific article; zbMATH DE number 96934