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模型的局部影响AI 解读

This article develops a general method for assessing the influence of model assumptions in a Bayesian analysis. We assume that model choices are indexed by a hyperparameter with some given initial choice. We use the term “model” to encompass both the sampling model and the prior distribution. We wish to assess the effect of changing the hyperparameter away from the initial choice. We are performing a sensitivity analysis, with the hyperparameter defining our perturbations.…

泊松回归模型中过度离散的检测检验AI 解读

Poisson regression models are widely used in analyzing count data. This article develops tests for detecting extra-Poisson variation in such situations. The tests can be obtained as score tests against arbitrary mixed Poisson alternatives and are generalizations of tests of Fisher (1950) and Collings and Margolin (1985). Accurate approximations for computing significance levels are given, and the power of the tests against negative binomial alternatives is compared with…

一般回归模型中条件无偏的有界影响估计及其广义线性模型应用AI 解读

In this article robust estimation in generalized linear models for the dependence of a response y on an explanatory variable x is studied. A subclass of the class of M estimators is defined by imposing the restriction that the score function must be conditionally unbiased, given x. Within this class of conditionally Fisher-consistent estimators, optimal bounded-influence estimators of regression parameters are identified, and their asymptotic properties are studied. The…

含随机效应与 AR(1) 误差的纵向数据模型AI 解读

For longitudinal data on several individuals, linear models that contain both random effects across individuals and autocorrelation in the within-individual errors are studied. A score test for autocorrelation in the within-individual errors for the “conditional independence” random effects model is first developed. An explicit maximum likelihood estimation procedure using the scoring method for the model with random effects and (autoregressive) AR(1) errors is then derived.…

多元二元时间序列的一类 logistic 回归模型AI 解读

A logistic model for multivariate binary time series is proposed. First, we establish the equivalence between a log-linear model for the marginal distribution of a multivariate binary random vector and logistic models for the conditional distributions of each component given the others. The logistic formulation is used to describe a Markov chain for each series, which implies a Markov model for the vector of time series. A pseudolikelihood estimation procedure is presented.…

牲畜调查总量的组合估计AI 解读

Four different preliminary estimators are employed by the National Agricultural Statistics Service of the U.S. Department of Agriculture to obtain the final estimate of livestock inventories of major states. To combine these four estimators a composite estimator (which is a weighted average) is proposed. Two types of composite estimators—one with fixed weights, the other with adaptive weights—are investigated. The composite estimator with adaptive weights is derived by…

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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…

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实验随机化与正态理论推断的有效性AI 解读

This article examines how randomization helps to validate model-based probability statements. The asymptotic validity of normal-theory tests for means in multivariate linear models is established under general conditions. Numerical results are presented showing how randomization provides a limited degree of robustness in small experiments. The conditional relevance of randomization is also discussed. Consider the following additive model for a comparative experiment: Y = θ +…

多元时间序列的自相关与随机性检验AI 解读

There exist several tests for autocorrelation and randomness in multiple time series. Unfortunately, the exact distributions of these statistics are unknown and the asymptotic distributions that are known do not provide adequate approximation to the exact ones in small samples. In this article, the test statistics are modified. Asymptotically, these modified statistics are equivalent to their original counterparts; however, it is found that the asymptotic distributions of…

利用独立结构改进列联表概率估计AI 解读

Estimation of the cell probabilities in a two-way contingency table is considered when it is plausible that the table might have an independence structure relating to the two traits. In a classical nonparametric setup, the unrestricted maximum likelihood estimators of the cell probabilities are the corresponding sample proportions; under the assumption of independence, the restricted estimators are the product of the respective row and column sample proportions. The latter…

量值估计中的受访者行为AI 解读

Some researchers argue that data obtained using magnitude estimation have metric properties superior to those of data obtained using traditional survey items. The analysis in this article examines evidence relevant to the assumptions that respondents can express ratios using numbers, can locate an internal continuum, and can use the standard stimulus effectively. The data are answers to 5 practice items designed to teach magnitude estimation using line lengths and up to 18…

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线性回归中的敏感性分析AI 解读

The Prediction Matrix Role of Variables in a Regression Equation Effects of an Observation on a Regression Equation Assessing the Influence of Multiple Observations Joint Impact of a Variable and an Observation Assessing the Effect of Errors of Measurements A Study of Model Sensitivity by the Generalized Linear Model Approach Computational Considerations. Appendix: Summary of Vector and Matrix Norms, Proofs of Three Theorems.