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一般混合与随机效应模型中基于小样本渐近的单侧及双侧容忍区间AI 解读

The computation of tolerance intervals in mixed and random effects models has not been satisfactorily addressed in a general setting when the data are unbalanced and/or when covariates are present. This article derives satisfactory one-sided and two-sided tolerance intervals in such a general scenario, by applying small-sample asymptotic procedures. In the case of one-sided tolerance limits, the problem reduces to the interval estimation of a percentile, and accurate…

实验室间比对中真值的模型与置信区间AI 解读

We consider the one-way random-effects model with unequal sample sizes and heterogeneous variances. Using the method of generalized confidence intervals, we develop a new confidence interval procedure for the mean. Additionally, we investigate two alternative models based on different sets of assumptions regarding between-group variability and derive generalized confidence interval procedures for the mean. These procedures are applicable to small samples. Statistical…

多元校准中的容忍域与可多次使用的置信域AI 解读

Let $\mathrm{y}~ N(Bx_i,\Sigma),i=1,2\ldots,N$, and $\mathrm{y}~N(B\theta, \Sigma)$ be independent multivariate observations, where the $x_i$'s are known vectors, $B,\theta$ and $\Sigma$ are unknown, $\Sigma$ being a positive definite matrix. The calibration problem deals with statistical inference concerning $\theta$ and the problem that we have addressed is the construction of confidence regions. In this article, we have constructed a region for $\theta$ based on a…

负值概率更低的改进方差分量估计量AI 解读

SUMMARY A linear model with two variance components is considered, one variance component (say, σ 1 2 ≥ 0) corresponding to a random effect, and a second variance component (say, σ 2 > 0) corresponding to the experimental errors. A class of invariant quadratic estimators (IQEs) is characterized, having uniformly smaller mean-squared error (MSE), and uniformly smaller probability of negativity, compared with the analysis-of-variance (ANOVA) estimator of σ 1 2. It turns out…

合并独立检验的若干统计程序AI 解读

In many applications available data from several independent studies address the same question, and it is essential to have statistical methods for combining the results from the different studies. This article addresses this issue in two setups: (1) a testing hypothesis concerning the common mean vector of two independent linear models having different variances, and (2) a testing hypothesis concerning a common variance component in linear models involving two variance…

线性模型中独立检验的合并AI 解读

A class of independent linear models is considered, where the variances of the different models are unequal but they have a common vector parameter θ occurring in their mean vectors. For testing the hypothesis H 0: θ = 0, some exact test procedures are derived that combine the information from all the models. The procedures are extensions of the test suggested by Cohen and Sackrowitz for recovering interblock information in balanced incomplete block designs. Simulation…

方差分量的最优无偏估计AI 解读

One: The Basic Model and the Estimation Problem.- 1.1 Introduction.- 1.2 An Example.- 1.3 The Matrix Formulation.- 1.4 The Estimation Criteria.- 1.5 Properties of the Criteria.- 1.6 Selection of Estimation Criteria.- Two: Basic Linear Technique.- 2.1 Introduction.- 2.2 The vec and mat Operators.- 2.3 Useful Properties of the Operators.- Three: Linearization of the Basic Model.- 3.1 Introduction.- 3.2 The First Linearization.- 3.3 Calculation of var(y).- 3.4 The Second…

无交互作用的不平衡双向模型中的最优检验AI 解读

It is an open problem in the literature to derive optimum tests for the equality of treatment effects in an unbalanced two-way classification model. For such models without interaction, optimum tests are derived in the following cases: (i) the locally best invariant unbiased test for the random effects model corresponding to an equiblock and equireplicate design, (ii) the locally best invariant unbiased test for the mixed effects model with mixed treatment effects…

平衡模型中固定效应与方差分量的最优检验AI 解读

For any analysis-of-variance model with balanced data involving both fixed and random effects, uniformly most powerful unbiased (UMPU) and uniformly most powerful invariant unbiased (UMPIU) tests are derived for the significance of a fixed effect or a variance component, under the assumption of normality of random effects. The tests coincide with the usual F tests. Robustness of the UMPIU test against suitable deviations from normality is established.

具有共同线性部分的模型中误设离散矩阵下的线性估计AI 解读

The linear model (Y, Xβ, V), where X is any matrix satisfying the conditions ℛ (U) ⊂ ℛ (X) and ℛ (A′) ⊂ ℛ (X′), is considered, U and A being known matrices and ℛ (·) denoting range space. Nonnegative definite matrices V, for which every linear representation or some linear representation of the BLUE of Aβ under (Y, Xβ, V 1) continues to be its BLUE under (Y, Xβ, V) for every such matrix X, are characterized. Conditions under which estimable linear parametric functions admit…

具有共同线性部分的线性模型中协方差误设下的线性估计AI 解读

The linear model (Y, Xβ, V), where X is any matrix satisfying the conditions ℛ (U) ⊂ ℛ (X) and ℛ (A′) ⊂ ℛ (X′), is considered, U and A being known matrices and ℛ (·) denoting range space. Nonnegative definite matrices V, for which every linear representation or some linear representation of the BLUE of Aβ under (Y, Xβ, V 1) continues to be its BLUE under (Y, Xβ, V) for every such matrix X, are characterized. Conditions under which estimable linear parametric functions admit…