Invariant confidence sequences for some parameters in a multivariate linear regression model (Q1058790)

Let \(X_{(n)}=(X_ 1,..., X_ n)\) be a random matrix with i.i.d. \(X_ i\sim N_ p(\beta Y_ i, \Sigma)\), where \(\beta\) : \(p\times q\) and \(\Sigma\) are unknown parameters. The paper derives a sequence of invariant (with respect to nonsingular matrices) subsets \(R_{(n)}(X_{(n)})\subset {\mathbb{R}}^{p\times q}\) with \(P(\cap_{n\geq m}R_{(n)}(X_{(n)})\ni \beta)\geq 1-\alpha\) for some fixed m. Some sub- parameters are also dealt with. Some special choices of p and q give known confidence sequences, some other choices result in solutions being simpler than the known ones.