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March, 1984 Invariant Confidence Sequences for Some Parameters in a Multivariate Linear Regression Model
B. K. Sinha, S. K. Sarkar
Ann. Statist. 12(1): 301-310 (March, 1984). DOI: 10.1214/aos/1176346408

Abstract

Let $\mathbf{X}_1, \mathbf{X}_2,\cdots$ be independent $p$-variate normal vectors with $E \mathbf{X}_\alpha \equiv \beta \mathbf{Y}_\alpha, \alpha = 1,2,\cdots$ and same p.d. dispersion matrix $\Sigma$. Here $\beta: p \times q$ and $\Sigma$ are unknown parameters and $\mathbf{Y}_\alpha$'s are known $q \times 1$ vectors. Writing $\beta = (\beta'_1 \beta'_2)' = (\beta_{(1)}\beta_{(2)})$ with $\beta_i: p_i \times q(p_1 + p_2 = p)$ and $\beta_{(i)}: p \times q_i(q_1 + q_2 = q)$, we have constructed invariant confidence sequences for (i) $\beta$, (ii) $\beta_{(1)}$, (iii) $\beta_1$ when $\beta_2 = 0$ and (iv) $\sigma^2 = |\Sigma|$. This uses the basic ideas of Robbins (1970) and generalizes some of his and Lai's (1976) results. In the process alternative simpler solutions of some of Khan's results (1978) are obtained.

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B. K. Sinha. S. K. Sarkar. "Invariant Confidence Sequences for Some Parameters in a Multivariate Linear Regression Model." Ann. Statist. 12 (1) 301 - 310, March, 1984. https://doi.org/10.1214/aos/1176346408

Information

Published: March, 1984
First available in Project Euclid: 12 April 2007

zbMATH: 0565.62018
MathSciNet: MR733515
Digital Object Identifier: 10.1214/aos/1176346408

Subjects:
Primary: 62F25
Secondary: 62H99, 62L10

Rights: Copyright © 1984 Institute of Mathematical Statistics

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Vol.12 • No. 1 • March, 1984
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