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受限参数空间下协方差矩阵的 REML 估计AI 解读

Restricted parameter spaces for covariance matrices, such as ∑ = σ2 I or ∑ = αI + βJ, are often used to simplify estimation. In addition, fixed upper and/or lower bounds may be needed to ensure that estimates satisfy a priori hypotheses. With multivariate variance components models, several covariance matrices need to be simultaneously estimated and, even with a reduced parameter space, estimation can be difficult. In earlier work we have discussed estimation for a…

Löwner 序约束下协方差矩阵的最大似然估计及其方差分量应用AI 解读

The problem of maximum likelihood estimation of Lowner ordered covariance matrices is considered. It is shown that a dual formulation of this problem is tractable and important in its own right. The interplay between the primal and dual problems suggests a general algorithm for computing the solutions to these problems. This algorithm has application to some estimation problems in balanced multivariate variance components models. The speed of convergence is also discussed…

平衡多变量方差分量模型中协方差矩阵的最小二乘估计AI 解读

The problem of estimating covariance matrices in balanced multivariate variance components models is discussed. As with univariate models, it is possible for the traditional estimators, based on differences of the mean square matrices, to produce estimates that are outside the parameter space. In fact, in many cases it is extremely likely that traditional estimates of the covariance matrices will not be nonnegative definite (nnd). In this article we develop an iterative…

平衡多元方差分量模型中协方差矩阵的最小二乘估计AI 解读

The problem of estimating covariance matrices in balanced multivariate variance components models is discussed. As with univariate models, it is possible for the traditional estimators, based on differences of the mean square matrices, to produce estimates that are outside the parameter space. In fact, in many cases it is extremely likely that traditional estimates of the covariance matrices will not be nonnegative definite (nnd). In this article we develop an iterative…

一般随机序约束下生存函数的非参数极大似然估计及其对偶AI 解读

This paper discusses estimation of survival functions under an arbitrary partial stochastic ordering of the underlying populations. This technique is especially useful when data are not easily acquired from one or more of the populations, but data from the other populations are available. Estimation of the ordered survival functions entails use of a Fenchel duality theorem that results in an algorithm to identify and resolve violations of the underlying ordering. The…

一般随机序约束下生存函数的非参数最大似然估计及其对偶AI 解读

This paper discusses estimation of survival functions under an arbitrary partial stochastic ordering of the underlying populations. This technique is especially useful when data are not easily acquired from one or more of the populations, but data from the other populations are available. Estimation of the ordered survival functions entails use of a Fenchel duality theorem that results in an algorithm to identify and resolve violations of the underlying ordering. The…

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N 个随机有序变量生存函数的极大似然估计AI 解读

Very often distributions will exist that logically should satisfy linear stochastic ordering requirements. For example, if a mechanical device is improved through N stages, the corresponding survival functions should be linearly stochastically ordered. Nevertheless, estimates may not totally reflect this stochastic ordering because of the inherent variability of the observations. Here we characterize the maximum likelihood estimates of the survival functions subject to…

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约束最小二乘回归的一种算法AI 解读

A commonly occurring problem in statistics is that of minimizing a least squares expression subject to side constraints. Here a simple iterative algorithm is presented and shown to converge to the desired solution. Several examples are presented, including finding the closest concave (convex) function to a set of points and other general quadratic programming problems. The dual problem to the basic problem is also discussed and a solution for it is given in terms of the…

Likelihood ratio statistics for (i) testing the homogeneity of a collection of multinomial parameters against the alternative which accounts for the restriction that those parameters are starshaped (cf. Shaked, Ann. Statist., 1979), and for (ii) testing the null hypothesis that this parameter vector is starshaped, are considered. For both tests the asymptotic distribution of the test statistic under the null hypothesis is a version of the Chi-bar-square distribution.…

两个及以上自变量的保序回归算法AI 解读

Algorithms for solving the isotonic regression problem in more than one dimension are difficult to implement because of the large number of lower sets present or because they involve search techniques which require a significant amount of checking and readjustment. Here a new algorithm for solving this problem based on a simple iterative technique is proposed and shown to converge to the correct solution.

随机有序变量生存函数的极大似然估计AI 解读

Many times, aspects of populations exist that must satisfy a stochastic ordering requirement. Nevertheless, estimates may not bear out this stochastic ordering because of the inherent variability of the observations. This article will consider the problem of finding maximum likelihood estimates of stochastically ordered survival functions for the cases (a) one survival function being fixed in advance and (b) estimating two survival functions when the data include censored…

多元方差分析中相互依赖的显著性检验AI 解读

It is shown that in the MANOVA situation, certain dependent tests of hypothesis may be combined to obtain an overall conservative significance level. The result holds whether one uses the Wilks, Roy, Lawley-Hotelling or Pillai test criterion. This generalizes a result due to Kimball in univariate ANOVA.

Wishart 矩阵特征根的正相依性AI 解读

It is shown that the characteristic roots of a Wishart matrix (identity covariance matrix) and the roots of $S_1 S_2^{-1}$ and $S_1(S_1 + S_2)^{-1}$ where $S_1, S_2$ are independent $p \times p$ Wishart matrices with the same covariance matrix, satisfy certain types of dependency relationships. That is, it is shown that these roots are (a) positive orthant dependent, (b) associated, (c) stochastically increasing in sequence, and (d) positively likelihood ratio dependent. An…

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一种二元 t 分布及其应用AI 解读

A particular bivariate t-distribution is defined and investigated. Included is a discussion of how to compute probabilities for this distribution. Applications involve the construction of double sample tests for hypotheses pertaining to the mean of a normal distribution with unknown variance. Some bounds are given for the error incurred when the two component variables are provisionally assumed to be independent.

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