Invariant Confidence Sequences for Some Parameters in a Multivariate Linear Regression Model

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.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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笔记与分组

分类依据与纠错

Invariant Confidence Sequences for Some Parameters in a Multivariate Linear Regression Model

代码、数据与补充材料

多元线性回归若干参数的不变置信序列

原文摘要

同方向的基础文献

同方向的基础文献