论文检索

多变量家庭数据的主成分分析AI 解读

The use of a principal component analysis is considered for multivariate data on families with different numbers of siblings. The coefficients in principal components are given as the eigenvectors of the weighted sums of squares and products matrix from the sibling data. Asymptotic distributions of the eigenvalues and eigenvectors of the estimated covariance matrix are obtained for an elliptical population. Asymptotic distributions of statistics associated with reduction of…

风险与生存分析中特定发生／暴露率的非参数估计AI 解读

A cohort of individuals exposed to some risk is followed up to a point of time M, and observations on two random variables (Y, Δ) are recorded for each individual. The variable Δ refers to one of the four possible events that can occur for an individual in the period [0, M]: (i) dies of a specific disease, say cancer, (ii) dies of a natural cause, (iii) withdraws from the study, and (iv) is alive and still under study at time M. The variable Y refers to the time at which an…

多元家庭数据的主成分分析AI 解读

The use of a principal component analysis is considered for multivariate data on families with different numbers of siblings. The coefficients in principal components are given as the eigenvectors of the weighted sums of squares and products matrix from the sibling data. Asymptotic distributions of the eigenvalues and eigenvectors of the estimated covariance matrix are obtained for an elliptical population. Asymptotic distributions of statistics associated with reduction of…

增长曲线模型中的协变量选择AI 解读

The growth curve model introduced by Potthoff & Roy (1964) is a generalization of the multivariate analysis of variance model and is often employed to analyze longitudinal data, in which a single characteristic has been measured at p different occasions on each individual. Inferential problems of this model are studied by using analysis of covariance, i.e. partitioning the p measurements into the measurements of q response variables and p-q covariables. Rao (1965, 1966) and…

样本均值函数的 Edgeworth 展开AI 解读

Many important statistics can be written as functions of sample means of vector variables. A fundamental contribution to the Edgeworth expansion for functions of sample means was made by Bhattacharya and Ghosh. In their work the crucial Cramer $c$-condition is assumed on the joint distribution of all the components of the vector variable. However, in many practical situations, only one or a few of the components satisfy (conditionally) this condition while the rest do not…

家族数据中多元类间与类内相关指标的推断AI 解读

SUMMARY Multivariate measures of interclass and intraclass correlations are introduced to assess the degree of resemblance between family members with respect to more than one characteristic. Unified estimators for the multivariate measures are proposed as the eigenvalues of certain random matrices constructed by the matrices of the weighted sums of squares and products of observations. Asymptotic distributions of the proposed estimators are derived under the assumption of…

增长曲线模型中的协变量选择AI 解读

The growth curve model introduced by Potthoff & Roy (1964) is a generalization of the multivariate analysis of variance model and is often employed to analyze longitudinal data, in which a single characteristic has been measured at p different occasions on each individual. Inferential problems of this model are studied by using analysis of covariance, i.e. partitioning the p measurements into the measurements of q response variables and p-q covariables. Rao (1965, 1966) and…

回归问题中强一致的模型选择程序AI 解读

We consider the multiple regression model Yn= Xnβ+ En, where Yn and En are n-vector random variables, Xn is an n×m matrix and β is an m-vector of unknown regression parameters. Each component of β may be zero or nonzero, which gives rise to 2m possible models for multiple regression. We provide a decision rule for the choice of a model which is strongly consistent for the true model as n →∞. The result is proved under certain mild conditions, for instance without assuming…

参数同时估计中单个估计量的精度AI 解读

Biases and mean squared errors of estimators of individual parameters are obtained for Stein type estimators of a vector parameter. It is known that for such estimators the average mean squared error over the different parameters under estimation is smaller than that for the usual unbiased estimators. However, such a property may not hold for the mean squared error of any individual estimator for the corresponding parameter. It is found that when a number of parameters are…

同时估计参数时单个估计量的精度AI 解读

Biases and mean squared errors of estimators of individual parameters are obtained for Stein type estimators of a vector parameter. It is known that for such estimators the average mean squared error over the different parameters under estimation is smaller than that for the usual unbiased estimators. However, such a property may not hold for the mean squared error of any individual estimator for the corresponding parameter. It is found that when a number of parameters are…

线性模型中的参数估计AI 解读

The first lecture in this series is devoted to a survey of contributions during the last five years to estimation of parameters by linear functions of observations in the Gauss-Markoff model. Some new results are also given. The classes of BLE (Bayes linear estimators) and ALE (admissible linear estimators) are characterized when the loss function is quadratic. It is shown that ALE's are either BLE's or limits of BLE's. Biased estimators like ridge and shrunken estimators…

摘要暂缺

投影算子、广义逆与最佳线性无偏估计AI 解读

Summary It is well known that in the Gauss–Markov model (Y, Xβ, σ2 V) with | V | ≠ 0, the BLUE (best linear unbiased estimator) of Xβ is Y1, the orthogonal projection of Y on M(X), the space spanned by the columns of X, with inner product defined as (x, y) = x'V-1 y. A quadratic function of Y2, the projection of Y on the orthogonal complement of M(X), provides an estimate of σ2. It may be seen that Y = Y1 + Y2. When V is singular, the inner product definition as in…

摘要暂缺

线性模型中方差与协方差分量的估计AI 解读

We write a linear model in the form , where is an unknown parameter and ξ is a hypothetical random variable with a given dispersion structure but containing unknown parameters called variance and covariance components. A new method of estimation called MINQUE (Minimum Norm Quadratic Unbiased Estimation) developed in a previous article [5] is extended for the estimation of variance and covariance components.

线性模型中的异方差方差估计AI 解读

Let Y=Xβ+e be a Gauss-Markoff linear model such that E(e) = 0 and D(e), the dispersion matrix of the error vector, is a diagonal matrix δ whose ith diagonal element is σi 2, the variance of the ith observation yi. Some of the σi 2 may be equal. The problem is to estimate all the different variances. In this article, a new method known as MINQUE (Minimum Norm Quadratic Unbiased Estimation) is introduced for the estimation of the heteroscedastic variances. This method…

摘要暂缺

摘要暂缺

摘要暂缺

矩阵广义逆及其在数理统计问题中的应用札记AI 解读

SUMMARY Some years ago the author defined a pseudo inverse of a singular matrix and used it in representing a solution of normal equations and for obtaining variances and covariances of estimates in the theory of least squares (Rao, 1955). This provided a unified approach to least squares theory, including the case when the normal equations become singular. This note attempts to collect a few mathematical results, some of which are known in literature, associated with the…

大样本中的有效估计与最优推断程序AI 解读

SUMMARY The concept of efficiency in estimation is linked with closeness of approximation to the derivative of log likelihood, which plays an important role in statistical inference in large samples. Various orders of efficiency are defined depending on degrees of closeness, and properties of estimates satisfying these criteria are studied. Such measures of efficiency appear to be more appropriate than the one related to asymptotic variance of an estimate for judging the…

摘要暂缺

摘要暂缺

单个变量观测不完整时的多元离散分析AI 解读

Summary In analysis of dispersion (multivariate generalization of the analysis of variance) Wilks' A criterion for testing hypotheses on all the multiple characters simultaneously cannot be applied if some observations on one or more of the characters are missing. In this article is provided a suitable criterion when data become incomplete due to missing observations in one of the characters only. This is the likelihood ratio criterion with a slight modification. The exact…