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Gauss–Markov 定理的非线性版本AI 解读

This article gives a nonlinear version of the Gauss—Markov theorem. It is shown that in a linear regression model y = Xβ + u, the lower bound for the risk matrix of a nonlinear estimator of β belonging to a certain class is the covariance matrix of the Gauss—Markov estimator, provided the distribution of error term u belongs to the class of elliptically symmetric distributions with second moments.

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能识别高生产率工人吗？稀疏双向表的稳健分析AI 解读

Data from individual measurements of production in a manufacturing environment may be thought of as a two-way table indexed by worker and task. If there are many tasks, such a table will normally be sparse. Adjustment for task effects is important if workers are to be compared to one another, since any two workers may have no tasks in common. Three techniques are presented for the analysis of such sparse tables: table-stripe regression, rectangle ratios, and network scores.…

Hildreth—Houck估计量的渐近分布AI 解读

Hildreth and Houck (1968) discussed a random-coefficients regression model and proposed several weighted least squares estimators with estimated weights. They conjectured that the estimators are asymptotically equivalent to the weighted least squares estimator with known weights. In this article the conjecture is verified, providing the first correct proof that Hildreth—Houck estimators are asymptotically normal. One of Hildreth and Houck's conditions is eliminated. An…

卡方拟合优度分析的非中心参数及其对数线性应用AI 解读

Limiting noncentral chi-squared distributions are obtained for statistics commonly used in sequential stepwise testing to select from a general class of functions the correct model for T multinomial cell frequencies in an m-way cross-classification table. The simple quadratic form expressions are used to establish the asymptotic independence of tests of nested models used in stepwise selection. In an application of these results, the quadratic form expression for the…

复杂抽样下的刀切法卡方检验AI 解读

Complex sample designs typically invalidate the direct application of the familiar Pearson or likelihood-ratio chi-squared statistics for testing the fit of a model to a cross-classified table of counts. This article discusses the adjustment of these statistics through a jackknifing approach. The technique may generally be applied whenever a standard replication method, such as the jackknife, bootstrap, or repeated half-samples, provides a consistent estimate of the…

Cox回归与一般条件似然的诊断方法AI 解读

Diagnostics for changes in the maximum likelihood estimate of β due to deletion of single observations in linear and logistic regression models are equivalent to diagnostics obtained from fitting augmented regression models. For the Cox proportional hazards model and in conditional models for arbitrarily matched or stratified data, diagnostics derived from augmented regression models are again useful and easy to compute. These diagnostics are applicable to different…

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,…

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多重社会关系的统计分析AI 解读

Loglinear models are adapted for the analysis of multivariate social networks, a set of sociometric relations among a group of actors. Models that focus on the similarities and differences between the relations and models that concentrate on individual actors are discussed. This approach allows for the partitioning of the actors into blocks or subgroups. Some ideas for combining these models are described, and the various models and computational methods are applied to the…

马尔可夫序列的非参数密度估计、预测与回归AI 解读

Let {Xi } be a stationary Markov sequence having a transition probability density function f(y | x) giving the pdf of X i +1 | (Xi = x). In this study, nonparametric density and regression techniques are employed to infer f(y | x) and m(x) = E[X i + 1 | Xi = x]. It is seen that under certain regularity and Markovian assumptions, the asymptotic convergence rate of the nonparametric estimator mn (x) to the predictor m(x) is the same as it would have been had the Xi 's been…

过度平滑的非参数密度估计AI 解读

The optimal histogram for a sample of size n from a density defined on the entire real line requires at least (2n)1/3 bins, under mild smoothness conditions. Similar bounds exist for the frequency polygon and kernel estimators. Values near these bounds give nearly optimal results for a variety of smooth densities, providing good, quick density estimates.

论 Krasker–Welsch 有界影响回归估计量AI 解读

Recently, Krasker and Welsch (1982) considered a class of bounded-influence regression estimators. They showed that within this class the so-called Krasker—Welsch estimator is the only solution to a first-order necessary condition for strong optimality, that is, for minimizing, in the sense of positive definiteness, the asymptotic covariance matrix. However, whether any strongly optimal estimator in fact exists remained an open question. In this article, an example is given…

三个或四个均值多重比较的精确同时置信区间AI 解读

A procedure for constructing exact simultaneous confidence intervals for a finite set of multiple comparisons among three or four groups is presented. These confidence intervals are hyperbolic and based on an unbiased estimator of the mean values having a normal distribution with covariance matrix σ2V, where V is an arbitrary known positive definite matrix. This procedure is used to study the amount of conservativeness of Tukey—Kramer intervals for pairwise comparisons in an…

结构化回归问题中的先验分布设定AI 解读

The problem of assessing the prior mean and covariance matrix of the vector of regression coefficients in the normal multiple linear regression model is considered. Arguments are advanced for using expectations regarding the form of the design matrix in specifying the prior for problems with a structure that can aid in specifying these expectations. This is illustrated with models having second-order terms. An example is given.

二项数据的贝叶斯方法及其在无应答问题中的应用AI 解读

In this article, Bayesian estimation methods for several binomial probabilities are studied by using a mixture of a product of beta prior distributions. Approximations to the posterior means and credible regions are derived. The results obtained are applied to a sample survey problem in which there is significant nonresponse.

复杂调查中访问员方差实验的最优设计AI 解读

Fellegi's (1974) improved method for estimating the interviewer component of correlated response variance is extended to l groups of k interviewer assignments for general multistage survey designs. Using a linear models approach suggestive of Hartley and Rao's (1978), the independence of the two estimators of interviewer variance is established and the forms of the variances of the estimators are derived. Then using 1980 census data to compute terms in the estimator…

由故障与随访记录非参数估计寿命分布AI 解读

This article deals with the estimation problem of the survival function of an industrial product in which the real operating time is different from its actual calendar time. In an observational study of the product, sometimes only the time until failure is observable from the repair requests made by the owner, but nonfailure times themselves are not. The generalized maximum likelihood estimator of the survival function is presented, and its consistency, asymptotic normality,…

正电子发射断层成像的统计模型AI 解读

Positron emission tomography (PET)—still in its research stages—is a technique that promises to open new medical frontiers by enabling physicians to study the metabolic activity of the body in a pictorial manner. Much as in X-ray transmission tomography and other modes of computerized tomography, the quality of the reconstructed image in PET is very sensitive to the mathematical algorithm to be used for reconstruction. In this article, we tailor a mathematical model to the…