Multivariate sequential analysis with linear boundaries

Abstract

Let $\{S_n=(X_n,W_n){\}}_{n\ge 0}$ be a random walk with $X_n\in \mathbb{R}$ and $W_n\in {\mathbb{R}}^m$. Let $\tau ={\tau }_a=\inf \{n:X_n>a\}$. The main results presented are two term asymptotic expansions for the joint distribution of $S_{\tau }$ and $\tau$ and the marginal distribution of $h(S_{\tau }/a,\tau /a)$ in the limit $a\to \infty$. These results are used to study the distribution of $t$-statistics in sequential experiments with sample size $\tau$, and to remove bias from confidence intervals based on Anscombe's theorem.

Published at http://dx.doi.org/10.1214/074921706000000608 in the IMS Lecture Notes--Monograph Series (http://www.imstat.org/publications/lecnotes.htm) by the Institute of Mathematical Statistics (http://www.imstat.org)

References in corpus (1)

• Corrected confidence intervals for secondary parameters following sequential tests

Cited by in corpus (1)

• Corrected confidence intervals for secondary parameters following sequential tests