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逆线性回归中观测数量的最优分配AI 解读

Consider the problem of estimating $x$ under the inverse linear regression model $Y_i = \alpha + \beta x_i + \varepsilon_i,\quad Z_j = \alpha + \beta x + \varepsilon_j'$ for $i = 1,\cdots, n,\cdots, j = 1,\cdots, m,\cdots,$ where $\{\varepsilon_i\}, \{\varepsilon_j'\}$ are two sequences of i.i.d. rv's with 0 means and finite variances, $\{x_i\}$ is a sequence of known constants and $\alpha, \beta, x$ are unknown parameters. For fixed $T = m + n$, this paper considers a…

两个正态总体均值与方差相等的检验AI 解读

Let X 1, …, X m and Y 1, …, Y n be two independent random samples from normal populations N(μ1, σ1 2) and N(μ2, σ2 2), respectively. The statistical problem is to test H 0: μ1 = μ2 and σ1 2 = σ2 2 against H a : μ1 ≠ μ2 or σ1 2 ≠ σ2 2. Using Fisher's method of combining two independent test statistics, we suggest a test and prove that it is asymptotically optimal in the sense of Bahadur efficiency.

两个正态总体均值与方差相等的检验AI 解读

Let X 1, …, X m and Y 1, …, Y n be two independent random samples from normal populations N(μ1, σ1 2) and N(μ2, σ2 2), respectively. The statistical problem is to test H 0: μ1 = μ2 and σ1 2 = σ2 2 against H a : μ1 ≠ μ2 or σ1 2 ≠ σ2 2. Using Fisher's method of combining two independent test statistics, we suggest a test and prove that it is asymptotically optimal in the sense of Bahadur efficiency.

逆线性回归问题的序贯解法AI 解读

In this note we apply the sequential theory developed by Chow and Robbins [1] and Gleser [3], [4] to the inverse linear regression problem. A two-stage sequential procedure has been proposed for the construction of a fixed-width confidence interval for $x$ (an unknown parameter). It is shown that the limiting probabilities of "correct decision" are equal to $P^\ast$ (pre-assigned).