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若干变分结果及其在多重推断中的应用AI 解读

Let $(\mathbf{M}, \mathbf{T}, \mathbf{S})$ be random matrices such that $\mathbf{M}$ and $\mathbf{S}$ are Hermitian positive definite almost everywhere. Let $\mathbf{M}_{(t)} = \lbrack m_{ij}; 1 \leqq i, j \leqq t\rbrack, \mathbf{S}_{(t)} = \lbrack s_{ij}; 1 \leqq i, j \leqq t\rbrack$ and $\mathbf{T}_{(r,s)} = \lbrack t_{ij}; 1 \leqq i \leqq r, 1 \leqq j \leqq s\rbrack$, and define $Q(r, s) = P\lbrack G((\mathbf{M}_{(r)})^{-\frac{1}{2}}\mathbf{T}_{(r,s)}(\mathbf{S}_{(s)}) ^{-\frac{1}{2}}) \leqq c\rbrack$…

线性假设检验的正态理论近似AI 解读

Let $\{\mathbf{y}_1, \cdots, \mathbf{y}_N\}$ be $N$ independent repetitions of an experiment for which $\mathscr{E}\mathbf{y} = \mathbf{X\beta}$ and $\mathscr{E}(\mathbf{y} - \mathbf{X\beta})(\mathbf{y} - \mathbf{X\beta} ' = \sigma^2\mathbf{I}$, where $\mathbf{X}$ is nonstochastic of full rank and $\mathbf{\beta'} = \lbrack \mathbf{\beta_1'}, \cdot, \mathbf{\beta}_r'\rbrack$ and $\sigma^2$ are unknown parameters. We investigate some large-sample properties of $N^{\frac{1}{2}} (\hat{\mathbf{\beta}}_N - \mathbf{\beta})$…