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截断回归斜率的非参数估计AI 解读

A nonparametric estimate $\beta^\ast$ is presented for the slope of a regression line $Y = \beta_0X + V$ subject to the truncation $Y \leq y_0$. This model is relevant to a cosmological controversy which concerns Hubble's Law in Astronomy. The estimate $\beta^\ast$ corresponds to the zero-crossing of a random function $S_n(\beta)$, which for each $\beta$ is a Mann-Whitney type of statistic designed to measure heterogeneity among the calculated residuals $Y - \beta X$. The…

次序统计量伴随变量的一般分布理论AI 解读

Let $(X_i, Y_i) (i = 1, 2, \cdots, n)$ be $n$ independent $\mathrm{rv}$'s from some bivariate distribution. If $X_{r:n}$ denotes the $r$th ordered $X$-variate, then the $Y$-variate $Y_{\lbrack r:n\rbrack}$ paired with $X_{r:n}$ is termed the concomitant of the $r$th order statistics. The exact and asymptotic distribution theory of $Y_{\lbrack r:n\rbrack}$ and of its rank are studied. The results obtained are applied to a prediction problem in a Round Robin tournament.

次序统计量伴随变量之秩的分布与期望AI 解读

Let $(X_i, Y_i)$ be $n$ independent rv's having a common bivariate distribution. When the $X_i$ are arranged in nondecreasing order as the order statistics $X_{r:n} (r = 1,2,\cdots, n)$, the $Y$-variate $Y_{\lbrack r:n\rbrack}$ paired with $X_{r:n}$ is termed the concomitant of the $r$th order statistic. The small-sample theory of the distribution and expected value of the rank $R_{r:n}$ of $Y_{\lbrack r:n\rbrack}$ is studied. In the special case of bivariate normality an…