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多元校准中的容忍域与可多次使用的置信域AI 解读

Let $\mathrm{y}~ N(Bx_i,\Sigma),i=1,2\ldots,N$, and $\mathrm{y}~N(B\theta, \Sigma)$ be independent multivariate observations, where the $x_i$'s are known vectors, $B,\theta$ and $\Sigma$ are unknown, $\Sigma$ being a positive definite matrix. The calibration problem deals with statistical inference concerning $\theta$ and the problem that we have addressed is the construction of confidence regions. In this article, we have constructed a region for $\theta$ based on a…

重新考察随机向量的集中椭球AI 解读

Alternative definitions of the concentration ellipsoid of a random vector are surveyed, and an extension of the concentration ellipsoid of Darmois is suggested as being the most convenient and natural definition. The advantage of the proposed definition in providing substantially simplified proofs of results in (linear) estimation theory is discussed, and is illustrated by new and short proofs of two key results. A not-so-well-known, but elementary, extremal representation…