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不平衡析因设计的统一非参数方法AI 解读

Motivated by questions arising from the field of statistical genetics, we consider the problem of testing main, nested, and interaction effects in unbalanced factorial designs. Based on the concept of composite linear rank statistics, a new notion of weighted rank is proposed. Asymptotic normality of weighted linear rank statistics is established under mild conditions, and consistent estimators are developed for the corresponding limiting covariance structure. A unified…

不完整数据下的有序备择检验AI 解读

In testing the null hypothesis of no treatment effects in a randomized block experiment, a researcher may restrict attention to an ordered alternative and thereby increase the power of his test. Jonckheere and later Page proposed such test statistics based on the Kendall and Spearman correlation coefficients. Motivated by notions of distance between permutations, we generalize Jonckheere's and Page's tests to the situation in which one or more observations are missing from…

不完整数据下有序备择假设的检验AI 解读

In testing the null hypothesis of no treatment effects in a randomized block experiment, a researcher may restrict attention to an ordered alternative and thereby increase the power of his test. Jonckheere and later Page proposed such test statistics based on the Kendall and Spearman correlation coefficients. Motivated by notions of distance between permutations, we generalize Jonckheere's and Page's tests to the situation in which one or more observations are missing from…

一致性度量的渐近理论：以平均 Kendall tau 为重点AI 解读

The problem of $n$ rankings is considered and the asymptotic distributions of measures of concordance based on rank correlations are derived under the null model of complete randomness. The Bahadur efficiencies of the measures are computed. A matrix analysis then reveals the asymptotic distribution and superior efficiency of average Kendall tau. Some interpretation of the results is also made.

截断参数的序贯估计AI 解读

Consider the problem of sequentially estimating the parameter θ of a uniform distribution on (0, θ). It is shown that if the loss is measured by squared error plus a linear cost function, and the prior on θ is given by a Pareto distribution, a simple heuristic procedure incurs an excess risk above the Bayes risk not greater than the cost of three observations. The result is extended to a wider class of distributions which includes the uniform and to a wide class of priors.

截断参数的序贯估计AI 解读

Consider the problem of sequentially estimating the parameter θ of a uniform distribution on (0, θ). It is shown that if the loss is measured by squared error plus a linear cost function, and the prior on θ is given by a Pareto distribution, a simple heuristic procedure incurs an excess risk above the Bayes risk not greater than the cost of three observations. The result is extended to a wider class of distributions which includes the uniform and to a wide class of priors.

贝叶斯序贯估计AI 解读

For fixed $\theta$, let $X_1, X_2, \cdots$ be a sequence of independent identically distributed random variables having density $f_\theta(x)$. Using a sequential Bayes decision theoretic approach we consider the problem of estimating any strictly monotone function $g(\theta)$ when the error incurred by a wrong estimate is measured by squared error loss and the sampling cost is $c$ units per observation. A heuristic stopping rule is suggested. It is shown that the excess risk…