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混合模型的残差诊断AI 解读

A sample is commonly modeled by a mixture distribution if the observations follow a common distribution, but the parameter of interest differs between observations. For example, we observe the lengths but not the ages of a sample offish. It may be reasonable to assume that length is normally distributed about an unknown mean that depends on the age of the fish. Provided there is more than one age class in the sample, then the data are distributed as a mixture of normals. In…

重复测量实验中允许时间异方差的 ARMA 协方差结构AI 解读

Rochon and Helms (1989) presented a model for analyzing repeated measures experiments. The general linear model was used to assess the influence of covariate information, and ARMA time series models were put forward to characterize the covariance matrix among the repeated measures. Practical experience has suggested, however, that the ARMA assumption of constant variances and autocovariances over time is too restrictive for many applications. For example, observations may be…

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…

具有嵌套误差结构的回归模型中的参数估计AI 解读

Restricted randomizations, similar to those in split-plot type experiments, often are adapted to assign quantitative treatment factors to experimental units. Such restrictions result in the experiment having a nested error structure. Sufficient conditions are presented under which ordinary least squares (OLS) estimates of regressor parameters are uniformly minimum variance unbiased (UMVU). If one designs experiments so that these conditions are satisfied, the analysis is…

多元回归中评估测量可靠性的重要性AI 解读

In many contexts involving multivariate linear regression models, some or all of the independent (predictor) variables are measured with error. It is argued that if the goal is to assess the relationship of the dependent variables to the true predictor variables, then it is important to determine the reliability matrix Λ of the measurement X of the vector of true predictors. If Λ is singular, then the slope matrix B is not identifiable. If Λ is nearly singular, then B cannot…

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机会的结构：概率逻辑与运算导论AI 解读

Introduction Common sense reduced to calculation The logic and arithmetic of compound probabilities Probability pathways and a first glance at the logic of probability assessment Binomial probabilities and the concept of sampling distributions The normal distribution-remarkable crossroad of fact and theory Some complex probability assessments based on the normal distribution A brief climb to one of the next higher levels: Student's t-distributions and the logic of estimation…

双因素混合模型的秩检验方法AI 解读

The test problem of fixed treatment effects is considered in the two-factor mixed model with interaction and unequal cell frequencies when the classical assumptions of normality do not hold. An explicit form of a test statistic is derived using a partial rank transform (ranking all observations within each block), and the asymptotic distribution of the statistic is determined under the assumption that the number of blocks tends to infinity and the cell frequencies are…

利用条件密度混合估计层级模型边际后验密度的方法AI 解读

A technique called quantile integration is proposed for the estimation of marginal posterior densities arising in Bayesian models having hierarchical representations. The method is based on approximating marginal densities as mixtures of conditional densities, where the conditioning variables are selected deterministically from the mixing distributions. The form of the approximation makes it easy to implement, and the resulting approximations are computationally efficient to…

多个终点下针对指定处理的假设检验AI 解读

The problem of comparing an identified treatment with K other treatments is considered in a multivariate setting. Many formulations of composite alternative hypotheses are possible. For example, one might wish to examine whether the identified treatment is superior to the other treatments on all components of the response vector (i.e., is uniformly best) or whether the identified treatment is better than each treatment on at least one component (i.e., is admissible). For…

多变量动态线性变量测量误差模型的可识别性AI 解读

This article considers multivariate causal transfer function systems with latent stationary inputs and outputs. Their observation is assumed to be disturbed by errors in variables (EV). The main identification results for such models so far consist of structure theory. Derived are descriptions of classes of EV transfer function systems compatible with given covariance structures of the observed variables under various causality constraints. The case of unique determination…

次序统计量与推断：估计方法AI 解读

List of Tables. List of Figures. Introduction. Basic Theory. Moments and Other Expected Values. Linear Estimation Based on Order Statistics. Maximum Likelihood Estimation. Approximate Maximum Likelihood Estimation. Optimal Linear Estimation Based on Selected Order Statistics. Cohen -Whitten Estimators: Using Order Statistics.Estimation in Regression Models. A Sample Completion Technique for Censored Samples. Bibliography. Index.

删失数据的尺度最小距离估计AI 解读

This article examines how the level of censoring affects the performance of estimators of scale that minimize a weighted Cramérvon Mises distance between the Kaplan-Meier product-limit estimator of the survival distribution function and an assumed model. The article shows that under certain conditions these estimators are asymptotically normal if the survival function is a member of the assumed scale family. Weights that minimize the asymptotic variance under these…

非独立同分布数据下弹着精度分位数的可行贝叶斯估计AI 解读

An important measure of accuracy for problems of directing projectiles at targets is the circular error probable (CEP), a bivariate version of a 50% quantile point. This article presents a Bayesian procedure for estimating CEP when the projectile impact measurements are not iid, which is the case of usual practical interest. Our interest in a Bayesian procedure is motivated by a desire to combine accuracy information from several different sources. Except for the simplest…

排序集样本的非参数两样本方法AI 解读

Ranked-set samples have been shown to lead to improved methods of estimation in parametric settings under specific distributional forms when actual measurement of the sample observations is difficult but ranking them is relatively easy. The earliest work with ranked-set data concentrated on estimating a population mean or variance. More recently, a ranked-set sample estimator of a cumulative distribution function was developed and used to obtain a simultaneous confidence…

利用虚拟观测构造异常值模型的贝叶斯因子AI 解读

Suppose we think that most observations in a sample have been generated from a distribution with density f(x) but we fear that a few outliers from a distribution with density g(x) may have contaminated our sample. In many situations, we might assume that f(x) is a density depending on a parameter θ and that g(x) is of the same form as f but with parameter θ + δ or θδ. A number of Bayesian models for this problem when f is normal have been discussed by Freeman. He points out…

约束贝叶斯估计及其应用AI 解读

Bayesian techniques are widely used in these days for simultaneous estimation of several parameters in compound decision problems. Often, however, the main objective is to produce an ensemble of parameter estimates whose histogram is in some sense close to the histogram of population parameters. This is for example the situation in subgroup analysis, where the problem is not only to estimate the different components of a parameter vector, but also to identify the parameters…

用扩展卡尔曼滤波估计多变量动态广义线性模型的后验众数AI 解读

A family of multivariate dynamic generalized linear models is introduced as a general framework for the analysis of time series with observations from the exponential family. Besides common conditionally Gaussian models, this article deals with univariate models for counted and binary data and, as the most interesting multivariate case, models for nonstationary multicategorical time series. For univariate responses, a related yet different class of models has been introduced…

随机删失数据的卡方拟合优度检验AI 解读

In this article, procedures analogous to Karl Pearson's well-known chi-squared goodness-of-fit test for a simple null hypothesis are developed under the random censorship model. It is shown that one straightforward analog of Pearson's statistic is diminished in applicability due to the form of its limiting distribution. This leads to the development of an asymptotically exact test based on a Wald-type statistic with a chi-squared limiting null distribution. This test is…

最小平方与最小中位平方拟合残差的模型误设诊断比较AI 解读

This article explores model misspecification diagnostics based on least squares and least median of squares fits. It shows that in some circumstances, least median of squares methods (or any other estimator with the exact fit property) fail to reveal an incorrectly specified mean function, but least squares methods succeed.