论文检索

Wishart 矩阵子式的矩AI 解读

For a random matrix following a Wishart distribution, we derive formulas for the expectation and the covariance matrix of compound matrices. The compound matrix of order m is populated by all m×m-minors of the Wishart matrix. Our results yield first and second moments of the minors of the sample covariance matrix for multivariate normal observations. This work is motivated by the fact that such minors arise in the expression of constraints on the covariance matrix in many…

矩阵变换的雅可比与矩阵变量函数AI 解读

Jacobians of matrix transformations Jacobians in orthogonal and related transformations Jacobians in the complex case transformations involving Eigenvalues and unitary matrices some special functions of matrix argument functions of matrix argument in the complex case.

多元正态分布极端观测值的相关分析AI 解读

In measuring visual acuity, the extremes of a set of normally distributed measures are of concern, together with one or more covariates. This leads to a model in which (X, Y 1, Y 2) are jointly normally distributed with Y 1, Y 2 exchangeable and (X, Y i ) having a common correlation. Inferential procedures are developed for correlations and linear regressions among X and the ordered Y values. This requires determination of the covariance matrix of X, Y (1) = min{Y 1, Y 2}…

随机变量的二次型：理论与应用AI 解读

Textbook for a one-semester graduate course for students specializing in mathematical statistics or in multivariate analysis, or reference for theoretical as well as applied statisticians, confines its discussion to quadratic forms and second degree polynomials in real normal random vectors and matr

多元分布族AI 解读

For many years there has been an interest in families of bivariate distributions with marginals as parameters. Genest and MacKay (1986a,b) showed that several such families that appear in the literature can be derived by a unified method. A similar conclusion is obtained in this article through the use of mixture models. These models might be regarded as multivariate proportional hazards models with random constants of proportionality. The mixture models are useful for two…

Cholesky 分解的最优等变估计量AI 解读

Every positive definite matrix $\Sigma$ has a unique Cholesky decomposition $\Sigma = \theta\theta'$, where $\theta$ is lower triangular with positive diagonal elements. Suppose that $S$ has a Wishart distribution with mean $n\Sigma$ and that $S$ has the Cholesky decomposition $S = XX'$. We show, for a variety of loss functions, that $XD$, where $D$ is diagonal, is a best equivariant estimator of $\theta$. Explicit expressions for $D$ are provided.

密度估计的半参数方法AI 解读

One method of fitting a parametric density function f(x, θ) is first to estimate θ by maximum likelihood, say, and then to estimate f(x, θ) by . On the other hand, when the parametric model does not hold, the true density f(x) may be estimated nonparametrically, as in the case of a kernel estimate . The key idea proposed is to fit a combination of the parametric and nonparametric estimates, namely where π (0 ≤ π ≤ 1) is unknown. The parameter π is estimated from the data,…

摘要暂缺

多元方差分量模型的极大似然估计与似然比准则AI 解读

Maximum likelihood estimators are obtained for multivariate components of variance models under the condition that the effect covariance matrix is positive semidefinite with a maximum rank. The rank of the estimator is random. The estimation procedure leads to a likelihood ratio test that the rank of the effect matrix is not greater than a given number against the alternative that the rank is not greater than a larger specified number. Linear structural relationship models…

考虑二分子组选择的 P 值调整AI 解读

Using a probability inequality, we show that if U = ([Udot], Ü), [Udot] = (U 1, …, U k), Ü = (U k + 1, …, U 2k ) has a multivariate normal distribution with mean vector zero and covariance matrices cov([Udot], [Udot]) = cov(Ü, Ü) = R, cov([Udot], Ü) = e'e – R, where R is a k × k correlation matrix and e = (1, …, 1), then P{|U 1| < c, …, |U 2k | < c} is minimized by setting all correlations in R equal to ½. This result is used to adjust the apparent significance of a…

摘要暂缺

二项分布试验次数的估计方法比较AI 解读

Estimating the number, n, of trials, given a sequence of independent success counts obtained by replicating the n-trial experiment is less studied and a considerably harder problem than estimating p for the binomial distribution. Both the method of moments and the maximum likelihood estimators of n are considered. When p is unknown and small, while n is large, both estimators become highly unstable. Stabilized versions of these estimators are proposed, and their performance…

摘要暂缺

一类误差相关的双向方差分析模型的最大似然估计AI 解读

A two-way analysis of variance model with correlated errors in one classification is discussed. It is assumed that the p measurements in each row have a general covariance matrix Σ The maximum likelihood estimates of the row and column parameters as well as of the covariance matrix are obtained and their asymptotic distribution are discussed. Finally, the likelihood ratio test statistics for the various hypotheses in a two-way layout are given.

多项分布与多个独立二项分布的可容许及极小极大估计AI 解读

Admissible and minimax estimation is discussed for estimating the parameters in the (a) multinomial distribution and in (b) $k$ independent binomial distributions. In (a) the loss function is $\sum^n_0\lbrack\delta_i(x) - \theta_i\rbrack^2/\theta_i$, where $\theta_0, \cdots, \theta_k(\sum\theta_i = 1)$ are the parameters in the multinomial distribution, and the estimators are restricted to $\sum^k_0\delta_i(x) = 1$. In (b) the loss functions considered are the weighted sum…

多元分布中的主序关系AI 解读

In case the joint density $f$ of $X = (X_1, \cdots, X_n)$ is Schur-concave (is an order-reversing function for the partial ordering of majorization), it is shown that $P(X \in A + \theta)$ is a Schur-concave function of $\theta$ whenever $A$ has a Schur-concave indicator function. More generally, the convolution of Schur-concave functions is Schur-concave. The condition that $f$ is Schur-concave implies that $X_1, \cdots, X_n$ are exchangeable. With exchangeability, the…

摘要暂缺

摘要暂缺

一种多元指数分布AI 解读

A number of multivariate exponential distributions are known, but they have not been obtained by methods that shed light on their applicability. This paper presents some meaningful derivations of a multivariate exponential distribution that serves to indicate conditions under which the distribution is appropriate. Two of these derivations are based on “shock models,” and one is based on the requirement that residual life is independent of age. It is significant that the…

摘要暂缺

摘要暂缺

摘要暂缺

关于《多元分析中若干有用矩阵变换的雅可比》的补注AI 解读

General techniques for the evaluation of the Jacobian of a matrix transformation were outlined by Deemer & Olkin (1951). In particular, (a) the Jacobian of a non-linear transformation is equal to the Jacobian of the linear transformation in the differentials, (b) by the introduction of suitable variables, the Jacobian is equal to a product of Jacobians which are easily calculated. This note is concerned with a number of transformations not considered in the earlier paper.…

摘要暂缺