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允许高剂量响应下降的剂量反应曲线非参数检验：渐近功效AI 解读

Dose-response experiments are widely used in scientific research and nonmonotone dose-response curves are commonly observed. A class of nonparametric tests for dose-response curves subject to downturns at high doses is examined via its asymptotic properties. This class includes the well-known Jonckheere-Terpstra test as a limiting case. The analysis indicates that the Jonckheere-Terpstra test lacks robustness to a downturn in the dose-response, and that other members of the…

Ames 沙门氏菌／微粒体致突变试验：推断与验证AI 解读

The importance of chemically induced mutation for human health is discussed briefly, and the biological basis for the primary in vitro assay for mutagenicity, the Ames Salmonella/microsome assay, is reviewed. A previous analysis for Ames test data, based on two mathematical models of the competing risks of mutation and toxicity, is shown to have inflated false-positive rates. A reason for this is the existence of local singularities in the Fisher information matrix. A new…

摘要暂缺

允许高剂量响应下降的剂量反应关系递归非参数检验AI 解读

A general recursive strategy is introduced to test nonparametrically for an increasing dose-response relationship when a downturn in response at high doses is possible. A specific implementation involving a test of Jonckheere (1954) and Terpstra (1952) is considered, and its size and power properties are investigated via Monte Carlo methods. Data from mutation research illustrate the phenomenon of concern.

非同分布观测下泊松假设的拟合优度检验AI 解读

Tests for detecting negative binomial departures from a Poisson model are studied for the one-way-layout and regression-through-the-origin cases. Approximations to the null and alternative distributions of these test statistics are presented. Locally optimal tests and tests suggested in the literature are compared in terms of asymptotic relative efficiency. Small sample comparisons are included.

多元正态离群值的检测AI 解读

The general outlier problem for a multivariate normal random sample with mean slippage is defined and is shown to be invariant under a natural group of transformations. A family of maximal invariants is obtained, and the common distribution of its members is derived. The critical region for the locally best invariant test of the null hypothesis, that there are no outliers, versus the alternative hypothesis, that some outliers are present, is found. Under very general…

多元容斥公式与相依随机变量的次序统计量AI 解读

A variant of the general multivariate inclusion-exclusion formula of Meyer (1969) is derived for the case where $K$ classes of events are considered and specific subsets of the events, one from each class, are related to one another by set inclusion. This result, in turn, yields a formula for the cumulative distribution function of any subset of order statistics from dependent random variables in terms of cumulative distribution functions of subsets of the unordered…

尺度未知的指数数据的 Kolmogorov–Smirnov 型检验及相关问题AI 解读

Let D^ , D^+ and D^− denote Kolmogorov-Smirnov typo one-sample statistics to test good ness of fit in the presence of unknown nuisance parameters; then the distributions of D^ , D^+ and D^− depend on the population sampled and the estimator used. Simulation has been the primary tool for studying these statistics. Recently, Durbin obtained the distributions of D^ , D^+ and D^− in terms of a Fourier transform for a wide class of underlying populations, and produced explicit…

未知尺度指数分布的 Kolmogorov–Smirnov 型检验及相关问题AI 解读

SUMMARY: Let D, D⁺ and D⁻ denote Kolmogorov-Smirnov typo one-sample statistics to test good ness of fit in the presence of unknown nuisance parameters; then the distributions of D, D⁺ and D⁻ depend on the population sampled and the estimator used. Simulation has been the primary tool for studying these statistics. Recently, Durbin obtained the distributions of D, D⁺ and D⁻ in terms of a Fourier transform for a wide class of underlying populations, and produced explicit…

分类数据的方差分析（二）：与卡方等方法的小样本比较AI 解读

Exact small sample behavior in two-way contingency tables is investigated for Pearson's chi-square statistic (X 2), Light and Margolin's C statistic and its related R 2 measure of association, Kullback's minimum discrimination information statistic (2Î), and Goodman and Kruskal's Lambda. R 2 is shown to be identical to Goodman and Kruskal's tb , leading to a test for independence based on tb. In small samples from a product of multinomials model, the null distribution of C…

分类数据的方差分析AI 解读

A measure of variation for categorical data is discussed. We develop an analysis of variance for a one-way table, where the response variable is categorical. The data can be viewed alternatively as falling in a two-dimensional contingency table with one margin fixed. Components of variation are derived, and their properties are investigated under a common multinomial model. Using these components, we propose a measure of the variation in the response variable explained by…

几何分布顺序统计量的精确矩及其与逆抽样和冗余系统可靠性的关系AI 解读

Formulae for the first two moments of the order statistics from a geometric distribution are presented in closed form. Brief illustrative tables of the first two moments of the order statistics from a geometric distribution are included and two related dice games are discussed. The distribution of the range of a set of independent observations from a geometric distribution is presented in closed form. A system of redundant components which performs a given task repetitively…

几何分布次序统计量的精确矩及其与逆抽样和冗余系统可靠性的联系AI 解读

Formulae for the first two moments of the order statistics from a geometric distribution are presented in closed form. Brief illustrative tables of the first two moments of the order statistics from a geometric distribution are included and two related dice games are discussed. The distribution of the range of a set of independent observations from a geometric distribution is presented in closed form. A system of redundant components which performs a given task repetitively…