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多元方差分量的改进非负定估计AI 解读

In this paper,we consider a multivariate one-way random effect model with equal replications. We propose nonnegative definite estimators for “between” and “within” components of variance. Under the Stein loss function, it is shown that the proposed estimators of the “within” component dominate the best unbiased estimator. Restricted maximum likelihood, truncated and order-preserving minimax estimators are also proposed. A Monte Carlo simulation is carried out to choose among…

椭圆分布下协方差矩阵估计的稳健改进AI 解读

This paper derives an extended version of the Haff or, more appropriately, Stein-Haff identity for an elliptically contoured distribution (ECD) . This identity is then used to show that the minimax estimators of the covariance matrix obtained under normal models remain robust under the ECD model.

布朗运动漂移变化检测中Shiryayev—Roberts程序的动态抽样AI 解读

In this paper, a dynamic sampling plan in the Shiryayev-Roberts procedure is considered. It is shown that a two-rate dynamic sampling plan is optimal in the sense that it minimizes the stationary average delay time (SADT). Analytical results as well as numerical comparisons show that it is significantly superior to the fixed sampling plan. The comparison also shows that it is as powerful as the dynamic sampling procedure of Assaf and Ritov. The generalizations to the fast…

均值偏移检测中 EWMA、CUSUM 与 Shiryayev–Roberts 方法的比较AI 解读

Pollak and Siegmund compared the Shiryayev-Roberts procedure with the CUSUM procedure for detecting a change in the drift of a Brownian motion based on the conditional average delay time. In this paper, the exponentially weighted moving average (EWMA) procedure proposed by Roberts is compared with the Shiryayev-Roberts and CUSUM procedures. The comparison is based on the stationary average delay time as advocated by Shiryayev. The optimal design for the EWMA procedure and…

多元分析中处理效应与误差的条件推断AI 解读

Directional methods of conditional inference are applied to the multivariate analysis of variance. Exact and easily implemented tests are derived for treatment effect, error variance matrix, and treatment improvement. Each test provides a physical measure of the magnitude of the departure from expectation under the hypothesis and is conditional on the indicated direction of departure. For treatment effect the test provides a geometrically understandable alternative to tests…

类间相关系数的渐近方差AI 解读

In genetics, the term interclass correlation has been used to refer to the parent-offspring and son-daughter correlations within families. Under the assumption of variable family sizes and normality, we derive the asymptotic variance of the maximum likelihood estimator of the son-daughter interclass correlation.

多元分析中处理效应与误差的条件推断AI 解读

Directional methods of conditional inference are applied to the multivariate analysis of variance. Exact and easily implemented tests are derived for treatment effect, error variance matrix, and treatment improvement. Each test provides a physical measure of the magnitude of the departure from expectation under the hypothesis and is conditional on the indicated direction of departure. For treatment effect the test provides a geometrically understandable alternative to tests…

In genetics, the term interclass correlation has been used to refer to the parent-offspring and son-daughter correlations within families. Under the assumption of variable family sizes and normality, we derive the asymptotic variance of the maximum likelihood estimator of the son-daughter interclass correlation.

类间相关系数的估计AI 解读

A noniterative method for estimating the interclass correlation coefficient is derived from the technique of weighted sums of squares. The asymptotic variance of this estimator is derived under the assumption of normality. Through extensive Monte Carlo simulations, the sample variance of this estimator is found not to differ greatly from that of the maximum likelihood estimator.

类间相关系数的估计AI 解读

A noniterative method for estimating the interclass correlation coefficient is derived from the technique of weighted sums of squares. The asymptotic variance of this estimator is derived under the assumption of normality. Through extensive Monte Carlo simulations, the sample variance of this estimator is found not to differ greatly from that of the maximum likelihood estimator.

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多元正态均值变化的似然比检验AI 解读

A sequence of independent multivariate normal vectors with equal but possibly unknown variance matrices are hypothesized to have equal mean vectors, and we wish to test that the mean vectors have changed after an unknown point in the sequence. The likelihood ratio test is based on the maximum Hotelling T 2 for the sequences before and after the change point. The main result is a conservative approximation for its null distribution based on an improved Bonferroni inequality.…

家庭数据中类间相关系数的估计AI 解读

The maximum likelihood estimates of the parent-child interclass correlation and other parameters from familial data when the families have unequal numbers of offspring is given. Also given are two alternative sets of estimates which are easier to compute than the maximum likelihood estimates. Using these estimates, a test for the interclass correlation to be zero requires only the ordinary Student's t-distribution. Similarly other tests use only known distributions.

家族数据中类间相关系数的估计AI 解读

SUMMARY The maximum likelihood estimates of the parent-child interclass correlation and other parameters from familial data when the families have unequal numbers of offspring is given. Also given are two alternative sets of estimates which are easier to compute than the maximum likelihood estimates. Using these estimates, a test for the interclass correlation to be zero requires only the ordinary Student's t-distribution. Similarly other tests use only known distributions.…

协方差矩阵似然比检验在非零假设下的分布渐近展开AI 解读

In this paper, asymptotic expansions of the non-null distributions of the likelihood ratio criteria are obtained for testing the hypotheses: (a) $H_1: \Sigma = \sigma^2I, \sigma^2 > 0$, (b) $H_2: \Sigma_1 = \Sigma_2$, against alternatives which are close to the hypothesis. These expansions are of chi-square type. The first problem has been considered by Sugiura (1969) but because of the singularity at the hypothesis, his expansion will not be good for alternatives close to…

基于 Wilcoxon 型估计的序贯置信区间AI 解读

For the location parameter family of distributions $F(x - \theta)$ under some regularity conditions, a confidence interval for $\theta$ of fixed width $2d$ and given confidence coefficient $1 - \alpha$ in the limit as $d$ tends to zero is obtained using Hodges-Lehmann estimates based on Wilcoxon statistics. An upper bound on the average sample size is also given.

类内相关模型中均值对比的 Tukey 置信区间AI 解读

Summary In the intraclass correlation model when the variance σ 2 and the intraclass correlation coefficient 'p are both unknown, Tukey's confidence intervals for the contrasts in the means are obtained for the fixed sample and the sequential case. In the latter case confidence intervals of fixed width are obtained and the cost of not knowing σ2 and ‘p has been studied. From these results parallel results for Scheffé's confidence intervals can easily be obtained. A…

滑移问题中一种序贯程序的性能AI 解读

Summary The basic problem known as a “Slippage problem” is to decide that none of the k experimental categories is better than the control or decide that a certain category is better. In this paper, a class of asymptotically efficient sequential procedures is proposed when both the error probabilities are controlled at a specified level (see also Srivastava, 1966). Assuming that these populations are normal with unknown variance σ2, the performance of the sequential…

Behrens–Fisher 问题的序贯对应形式AI 解读

Summary Srivastava (1966) proposed a class of asymptotically efficient sequential procedures for an analogue of the Behrens–Fisher problem. Recently, Robbins et al. (1967) also proposed the same class of sequential procedures. The object of this note is to give the details of our proof for the asymptotic efficiency, assuming only the finiteness of the variances. The multivariate analogue of this problem has also been considered.

回归参数与均值向量的固定宽度置信界AI 解读

Summary In this paper Chow and Robbins's (1965) sequential theory has been extended to construct a confidence region with prescribed maximum width and prescribed coverage probability for (i) the linear regression parameters, and (ii) the mean vector of a multivariate population. Except for the finiteness of the unknown variance and covariances in the respective two cases, no assumption regarding the form of their distribution functions is made. This result was announced in…

排序与滑移问题的若干渐近有效序贯程序AI 解读

Summary In this paper Chow and Robbins's (1965) sequential theory has been applied to ranking and slippage problems (including a multivariate slippage problem) and a class of asymptotically efficient sequential procedures is given for each problem. Except for the finiteness of the variance, no assumption regarding the form of the distribution function is made.