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右删失下两样本问题的条件分布无关检验AI 解读

Two-sample rank tests for survival data in the presence of arbitrary right censoring are considered. We distinguish between administrative censoring, arising because survival study participants do not enter as a cohort, and censoring due to “loss to follow-up.” We show how conditionally distribution-free tests can be constructed in certain situations. Conditional versions of the generalized Wilcoxon and Mantel statistics are shown to be asymptotically normal in the…

右删失下两样本问题的条件分布无关检验AI 解读

Two-sample rank tests for survival data in the presence of arbitrary right censoring are considered. We distinguish between administrative censoring, arising because survival study participants do not enter as a cohort, and censoring due to “loss to follow-up.” We show how conditionally distribution-free tests can be constructed in certain situations. Conditional versions of the generalized Wilcoxon and Mantel statistics are shown to be asymptotically normal in the…

累积生存数据的删失 Wilcoxon 两样本检验中的提前决策AI 解读

For two-sample testing problems, in which observations are collected in order of size, Ailing [1] showed that it is possible to determine the outcome of an uncensored Wilcoxon test well before data collection is complete. This article studies a similar problem for a censoring scheme terminating the experiment when a specified percentage of events has occurred in either group. The asymptotic distributions (null and nonnull) of the test statistic (of Wilcoxon type) and of the…

两个变量均有测量误差时的直线回归估计札记AI 解读

Let yi = α + βxi + εis xi = ξi + δis i = 1, 2, ···, N, N ≥ 3, where (εis δi)s i = 1, 2, ···, N are independent bivariate normal with zero means, variances σ ε2 σδ2 and correlation ρ, the ξi being unknown constants at least two of which are distinct. Let τ = (N−1)−1 ΣN i=1 (ξi − ξ)2/Σ δ2 and let . A recent article by Richardson and Wu gives, among other things, the expected value and m.s. error of b, when ρ = 0. This note generalizes their results, using a different method,…

两个变量均含误差时直线回归估计的一则说明AI 解读

Let yi = α + βxi + εis xi = ξi + δis i = 1, 2, ···, N, N ≥ 3, where (εis δi)s i = 1, 2, ···, N are independent bivariate normal with zero means, variances σ ε2 σδ2 and correlation ρ, the ξi being unknown constants at least two of which are distinct. Let τ = (N−1)−1 ΣN i=1 (ξi − ξ)2/Σ δ2 and let . A recent article by Richardson and Wu gives, among other things, the expected value and m.s. error of b, when ρ = 0. This note generalizes their results, using a different method,…

自变量取值受限时线性回归的置信带AI 解读

Several writers have studied the problem of obtaining confidence bands for a straight line regression under the requirement that the bands be at a specified confidence level, (1 – α) say, for values of the independent variable restricted to a pre-specified closed interval. The bands studied by other writers have been either bands of equal width throughout the interval or trapezoidal bands. This paper studies confidence bands of the classical hyperbolic type under the…

线性回归中更窄的置信带AI 解读

In many linear regression problems, the values of the independent variable or variables may be subject to certain constraints. For example, the independent variables may necessarily be positive; as another example, the variables may not only all be positive but are powers of a single variable (e.g., polynomial regression on time). Previous writers considering the problem of obtaining confidence bands on a regression function for all values of the independent variable have…

线性回归中更窄的置信带AI 解读

In many linear regression problems, the values of the independent variable or variables may be subject to certain constraints. For example, the independent variables may necessarily be positive; as another example, the variables may not only all be positive but are powers of a single variable (e.g., polynomial regression on time). Previous writers considering the problem of obtaining confidence bands on a regression function for all values of the independent variable have…

非线性参数函数的区间估计（三）AI 解读

Let f(μ1, μ2) = constant be a function which is monotone and has no finite termini in the (μ1, μ2) plane. Let x 1 and x 2 be either independent normal with unknown means μ1, μ2 and unknown variances σ2 1, σ2 2 or correlated normal with unknown mean vector (μ1, μ2) and unknown variance matrix σ. Suppose, in the first instance, that estimates, s 2 1 and s 2 2, of σ2 1 and σ2 2 with v 1 and v 2 degrees of freedom are available and, in the second instance, an estimate, S, of σ…

非线性参数函数的区间估计（三）AI 解读

Let f(μ1, μ2) = constant be a function which is monotone and has no finite termini in the (μ1, μ2) plane. Let x 1 and x 2 be either independent normal with unknown means μ1, μ2 and unknown variances σ2 1, σ2 2 or correlated normal with unknown mean vector (μ1, μ2) and unknown variance matrix σ. Suppose, in the first instance, that estimates, s 2 1 and s 2 2, of σ2 1 and σ2 2 with v 1 and v 2 degrees of freedom are available and, in the second instance, an estimate, S, of σ…

两个变量均含误差时线性回归的区间估计AI 解读

Define the linear functional relationship with parameters, α, β, by μ = α + βv. This paper considers the problem of confidence interval estimation of α and β separately, based on a sample of independent pairs, (x i , y i ), i = 1, 2, ···, n, with Ex i = vi, Ey i = μ i . The pairs, (x i , y i ), are assumed to be independent (i ≠ i′), to have a common (unknown) covariance matrix Σ, and to follow the bivariate normal distribution. It is known that under these circumstances…

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响应相关时非线性回归区间估计的说明AI 解读

Summary Recent papers by Williams and Halperin discuss procedures for obtaining confidence regions† for parameters in non-linear regression. These results assume, among other things, independence and homoscedasticity of variance of the dependent variables. This note points out that by using some results of Rao it is possible to drop these latter assumptions.

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非线性参数函数的区间估计AI 解读

Suppose x 1 and x 2 are observations on a bivariate normal distribution with known variance matrix Σ and unknown means vector (μ1, μ2). Suppose an interval estimate of f(μ 1, μ2), is desired with 1 – α confidence. Let an interval estimate be obtained as [min f(μ1, μ2), max f(μ1, μ2)] subject to [(x 1 – μ1) (x 2 – μ2)] Σ−1[(x 1 – μ1)(x 2 – μ2)]′ ≤ R 2. It is shown that under certain conditions on f(μ1, μ2) and Σ, R need be taken only slightly larger than x 1(α), the value of…

非线性参数函数的区间估计AI 解读

Suppose x 1 and x 2 are observations on a bivariate normal distribution with known variance matrix Σ and unknown means vector (μ1, μ2). Suppose an interval estimate of f(μ 1, μ2), is desired with 1 – α confidence. Let an interval estimate be obtained as [min f(μ1, μ2), max f(μ1, μ2)] subject to [(x 1 – μ1) (x 2 – μ2)] Σ−1[(x 1 – μ1)(x 2 – μ2)]′ ≤ R 2. It is shown that under certain conditions on f(μ1, μ2) and Σ, R need be taken only slightly larger than x 1(α), the value of…

非线性回归中的置信区间估计AI 解读

SUMMARY In a recent paper, E. J. Williams presents a procedure for obtaining what are described as fiducial intervals and regions for the non-linear parameters in non-linear regression. The linear parameters are not included in the regions which are developed and the class of non-linear regression functions for which his results hold is not clearly delineated. In this paper, it is shown how some results from standard regression theory can be used to discuss these points; the…

双变量均含误差时的直线拟合与预测AI 解读

Define the linear structural relation with parameters α, β, by μ = α +βv. This paper considers the problem of confidence region estimation of α and β based on a sample of independent pairs, (y i , x i ), i = 1, 2, ···, with Ey i = μi, Ex i = v i . The pairs (y i , x i ) are assumed to have a common (unknown) covariance matrix and to follow the bivariate normal distribution. Point estimates subject only to and that the choice of the l i be independent of the actual…

两个变量均含误差时的直线拟合与预测AI 解读

Define the linear structural relation with parameters α, β, by μ = α +βv. This paper considers the problem of confidence region estimation of α and β based on a sample of independent pairs, (y i , x i ), i = 1, 2, ···, with Ey i = μi, Ex i = v i . The pairs (y i , x i ) are assumed to have a common (unknown) covariance matrix and to follow the bivariate normal distribution. Point estimates subject only to and that the choice of the l i be independent of the actual…

Wilcoxon–Mann–Whitney检验对同一固定点删失样本的扩展AI 解读

A two-sample non-parametric significance test for censored samples is presented. The null hypothesis considered is that the two samples are from the same population. Tables of lower 5% and 1% points of the test statistic are given for both sample sizes ≦8 and various degrees of censoring. The asymptotic distribution of the test statistic under the null hypothesis is derived and numerical comparisons are given which indicate the asymptotic theory is adequate outside the range…

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截断正态分布中的估计AI 解读

Charts are presented which can be used to simplify estimation of μ and σ in the case of sampling from a singly truncated normal distribution when (a) the point of truncation and the number of observations in the truncated portion are known, (b) the number of observations in the truncated portion is not known. A somewhat different iteration procedure for case (a) than given by other writers is suggested and an example is given.