The Annals of Statistics

An Error Bound for an Asymptotic Expansion of the Distribution Function of an Estimate in a Multivariate Linear Model

Yasunori Fujikoshi

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Abstract

In this paper we consider asymptotic approximations to the distribution function $F(x)$ of a linear combination of an estimate in a multivariate linear model. A method is given for obtaining an asymptotic expansion $F_{s - 1}(x)$ of $F(x)$ up to $O(n^{-s + 1})$ and a bound $c_s$ such that $|F(x) - F_{s - 1}(x)| \leq c_s$ uniformly in $x$ and $c_s = O(n^{-s})$.

Article information

Source
Ann. Statist., Volume 13, Number 2 (1985), 827-831.

Dates
First available in Project Euclid: 12 April 2007

Permanent link to this document
https://projecteuclid.org/euclid.aos/1176349562

Digital Object Identifier
doi:10.1214/aos/1176349562

Mathematical Reviews number (MathSciNet)
MR790580

Zentralblatt MATH identifier
0576.62026

JSTOR
links.jstor.org

Subjects
Primary: 62E20: Asymptotic distribution theory
Secondary: 62H10: Distribution of statistics

Keywords
Error bound asymptotic expansion distribution function linear combination of an estimate multivariate linear model

Citation

Fujikoshi, Yasunori. An Error Bound for an Asymptotic Expansion of the Distribution Function of an Estimate in a Multivariate Linear Model. Ann. Statist. 13 (1985), no. 2, 827--831. doi:10.1214/aos/1176349562. https://projecteuclid.org/euclid.aos/1176349562


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