## 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

#### 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

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