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摘要暂缺

一般线性模型下估计或预测的均方误差AI 解读

The problem considered is that of predicting a linear combination of the fixed and random effects of a mixed-effects linear model. More generally, the problem considered is that of predicting an unobservable random variable from a set of observable random variables. The best linear-unbiased predictor depends on parameters which generally are unknown. Various exact or approximate expressions are given for the mean squared error (MSE) of the predictor obtained by replacing the…

非平衡混合线性模型方差分量的精确置信集AI 解读

We present a general procedure for obtaining an exact confidence set for the variance components in a mixed linear model. The procedure can be viewed as a generalization of the ANOVA method used with balanced models. Our procedure uses, as pivotal quantities, quadratic forms that are distributed independently as chi-squared variables. These quadratic forms are constructed with reference to spaces that are orthogonal with respect to the covariance matrix of the observation…

比较实验与小区域估计中的贝叶斯及非贝叶斯程序：计算、频率学性质与联系AI 解读

The estimation of a treatment contrast from experimental data and the estimation of a small-area mean are special cases of the prediction of the realization of a linear combination of fixed and random effects in a possibly unbalanced two-part mixed linear model. In this article a Bayesian approach to point and interval prediction is presented and its computational requirements are examined. Differences between the Bayesian approach and the traditional (classical) approach…

Wald 置信区间与检验的若干替代方法AI 解读

The problem considered is that of inference for the variance ratio λ = σ 2 s /σ 2 e in mixed linear models of the form y = Xβ + Zs + e, where β is a column vector of unknown parameters and s and e are statistically independent, multivariate-normal random vectors, with E(s) = 0, var(s) = σ 2 s I, E(e) = 0, and var(e) = σ 2 e I. The case where there is a known upper bound on λ is emphasized. The 100(1 α α)% confidence sets, corresponding to the following two-sided tests of the…

Wald 置信区间与检验的若干替代方法AI 解读

The problem considered is that of inference for the variance ratio λ = σ 2 s /σ 2 e in mixed linear models of the form y = Xβ + Zs + e, where β is a column vector of unknown parameters and s and e are statistically independent, multivariate-normal random vectors, with E(s) = 0, var(s) = σ 2 s I, E(e) = 0, and var(e) = σ 2 e I. The case where there is a known upper bound on λ is emphasized. The 100(1 α α)% confidence sets, corresponding to the following two-sided tests of the…

田间小区试验中 Papadakis 及其他非线性处理对比估计量的无偏性AI 解读

Spatial methods for the analysis of field-plot experiments are considered. Estimators of treatment contrasts obtained by these methods are generally complicated nonlinear functions of the observations. Sufficient conditions for these estimators to be unbiased under a postulated true model are obtained.

田间小区实验中 Papadakis 及其他非线性处理对比估计量的无偏性AI 解读

Spatial methods for the analysis of field-plot experiments are considered. Estimators of treatment contrasts obtained by these methods are generally complicated nonlinear functions of the observations. Sufficient conditions for these estimators to be unbiased under a postulated true model are obtained.

预测误差的分解AI 解读

The problem considered is that of predicting the value of an unobservable random variable w from the value of an observable random vector y. This problem is considered under each of four states of knowledge about the joint distribution of w and y, ranging from complete knowledge to “no” knowledge. A (point) predictor or predictors are presented for each case. Prediction error is decomposed so that each component reflects an absence of information. Under certain conditions,…

混合线性模型中固定与随机效应估计标准误的近似AI 解读

Best linear unbiased estimators of the fixed and random effects of mixed linear models are available when the true values of the variance ratios are known. If the true values are replaced by estimated values, the mean squared errors of the estimators of the fixed and random effects increase in size. The magnitude of this increase is investigated, and a general approximation is proposed. The performance of this approximation is investigated in the context of (a) the…

摘要暂缺

混合线性模型的最佳线性递归估计AI 解读

Recursive estimation techniques for fixed and completely random models are extended to mixed linear models. The Kalman filter is used to obtain recursive estimators for a two-part random model where the second random factor obeys a generalized autoregressive process. By passing to the limit in an appropriate way, recursions for the mixed model are derived.

任意协方差结构下固定线性模型可估函数的无偏与最小方差无偏估计AI 解读

Consider a general linear model for a column vector $y$ of data having $E(y) = X \alpha$ and $\operatorname{Var}(y) = \sigma^2H$, where $\alpha$ is a vector of unknown parameters and $X$ and $H$ are given matrices that are possibly deficient in rank. Let $b = Ty$, where $T$ is any matrix of maximum rank such that $TH = \phi$. The estimation of a linear function of $\alpha$ by functions of the form $c + a'y$, where $c$ and $a$ are permitted to depend on $b$, is investigated.…

约束混合模型估计的若干实用表示AI 解读

Mixed-model computations can be accomplished efficiently by using the Henderson mixed-model equations. An augmented version of the equations is developed for the case where there are constraints on the fixed effects. Equations comparable to the conjugate normal equations are also developed. These equations are useful for direct computation and, in the case of patterned designs, lend themselves well to algebraic simplification.

约束混合模型估计的若干实用表示AI 解读

Mixed-model computations can be accomplished efficiently by using the Henderson mixed-model equations. An augmented version of the equations is developed for the case where there are constraints on the fixed effects. Equations comparable to the conjugate normal equations are also developed. These equations are useful for direct computation and, in the case of patterned designs, lend themselves well to algebraic simplification.

方差分量估计及相关问题的极大似然方法AI 解读

Recent developments promise to increase greatly the popularity of maximum likelihood (ml) as a technique for estimating variance components. Patterson and Thompson (1971) proposed a restricted maximum likelihood (reml) approach which takes into account the loss in degrees of freedom resulting from estimating fixed effects. Miller (1973) developed a satisfactory asymptotic theory for ml estimators of variance components. There are many iterative algorithms that can be…

摘要暂缺

单向分类模型中方差分量的二次无偏估计AI 解读

The paper deals with the quadratic estimation of the components of variance associated with the one-way random classification where the effects are taken to be indepently and normally distributed and where the class numbers are unequal. An estimator is said to be inquadmissible or quadmissible depending on whether or not there exists a second quadratic estimator having the same expectation and smaller variance. A quadratric estimator is shown to be quadmissible only if it is…

单向分类模型中方差分量的二次无偏估计AI 解读

The paper deals with the quadratic estimation of the components of variance associated with the one-way random classification where the effects are taken to be indepently and normally distributed and where the class numbers are unequal. An estimator is said to be inquadmissible or quadmissible depending on whether or not there exists a second quadratic estimator having the same expectation and smaller variance. A quadratric estimator is shown to be quadmissible only if it is…

双向完全随机分类中子组均值与子组观测数的统计依赖AI 解读

This paper deals with certain aspects of variance-component estimation for the unbalanced two-way completely-random classification where the numbers of observations in the subclasses are treated as random variables not necessarily independent of some of the random effects of the model. General results are given on the expectations of two commonly-used estimators of the vector of variance components. Numerical approximations are presented for these expectations for one…

双向完全随机分类中子类均值与观测数量的统计依赖AI 解读

This paper deals with certain aspects of variance-component estimation for the unbalanced two-way completely-random classification where the numbers of observations in the subclasses are treated as random variables not necessarily independent of some of the random effects of the model. General results are given on the expectations of two commonly-used estimators of the vector of variance components. Numerical approximations are presented for these expectations for one…

非平衡单因素随机分类中随机效应与观测数量的统计依赖AI 解读

This paper deals with certain aspects of variance component estimation for the unbalanced one-way random classification where the number (Ni ) of observations in the ith class is treated as a random variable not necessarily independent of the class effect (Ai ). It is assumed that in general P(Ni = 0) > 0. The conditional expectations (given the number of observations in each class) of all estimators of the between variance component (σ2 a ) belonging to a certain class of…

不平衡单向随机分类中随机效应与观测数量的统计依赖AI 解读

This paper deals with certain aspects of variance component estimation for the unbalanced one-way random classification where the number (Ni ) of observations in the ith class is treated as a random variable not necessarily independent of the class effect (Ai ). It is assumed that in general P(Ni = 0) > 0. The conditional expectations (given the number of observations in each class) of all estimators of the between variance component (σ2 a ) belonging to a certain class of…