Multivariate sequential analysis with linear boundaries

Details Multivariate sequential analysis with linear boundaries Multivariate sequential analysis with linear boundaries

2006-11-22

arxiv.org/abs/math/0611678v1

IMS Lecture Notes--Monograph Series 2006, Vol. 50, 58-79

Mathematics

Statistics Theory

Published at http://dx.doi.org/10.1214/074921706000000608 in the IMS Lecture Notes--Monograph Series (http://www.imstat.org/

Scientific paper

10.1214/074921706000000608

Let $\{S_n=(X_n,W_n)\}_{n\ge0}$ 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.

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