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分组数据的稳健估计AI 解读

Here we investigate the robustness properties of the class of minimum power divergence estimators for grouped data. This class contains the classical maximum likelihood estimators for grouped data. We find that the bias of these estimators due to deviations from the assumed underlying model can be large. Therefore, we propose a more general class of estimators that allows us to construct robust procedures. By analogy with Hampel's theorem, we define optimal bounded influence…

区分优劣处理的最优划分程序AI 解读

This article considers partitioning a given set of competing treatments into two subsets with the purpose of separating good and bad treatments. (The qualities “good” and “bad” are defined in terms of the parameter vector of the underlying distribution family.) Regarding the probability of an incorrect partition, within the class of so-called natural procedures minimax solutions are derived under suitable distributional assumptions. These results extend previous…

正态均值的乘积分割模型AI 解读

I consider probability models for the estimation of normal means that allow for some of the means to be equal. These probability models, called product partition models, specify prior probabilities for a random partition. The posterior probability of the partition given the observations has the same form. The resulting estimate of the means—the product estimate—is obtained by conditioning on the partition and summing over all possible partitions. The large number of…

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混合线性模型中的有界影响估计AI 解读

Bounded influence estimation (also known as generalized M or GM estimation) in the regression model is reviewed. The definitions of bounded influence estimation proposed by Mallows and Schweppe are then extended to the mixed linear model. This is achieved by applying appropriate weight functions to maximum likelihood and restricted maximum likelihood estimating equations. The asymptotic properties of the new estimators are obtained, and the estimators are applied to an…

简化单调回归方法AI 解读

Medical researchers often desire to categorize patients into monotonic response groups based on the relationship between continuous variables. Isotonic regression fits consist of level sets of increasing value, for which the estimated response is constant. However, the number of level sets obtained is often large, preventing simple description. This article introduces two new nonparametric methods called reduced isotonic regression and reduced monotonic regression, the…

由含噪支持函数数据估计凸集AI 解读

In problems of medical imaging and robotic vision, measurements of a convex set are sometimes obtained via the set's support function. The standard way in which the convex set is recovered from such data is to suppose that it is polygonal, model the errors as Normal random variables, and apply constrained maximum likelihood methods. Typically, the number of sides assumed of the polygon is equal to or a little less than the number of data points. However, from a statistical…

响应曲线的加速时间模型AI 解读

We propose a nonparametric method of data analysis for situations where the data consist of a sample of curves and a covariate is present. We assume the observed curves to be time-accelerated versions of a basic underlying stochastic process and assume the time acceleration factor for each observed process, determining the “eigenzeit,” to be a smooth function of the covariate. We discuss an iterative procedure to estimate the components of the model nonparametrically, using…

利用多个二元结局研究致畸作用的潜变量模型AI 解读

Multiple outcomes are commonly measured in the study of birth defects. The reason is that most teratogens do not cause a single, uniquely defined defect, but rather result in a range of effects, including major malformations, minor anomalies, and deficiencies in birth weight, length and head circumference. The spectrum of effects associated with a particular teratogen is sometimes described as a “syndrome.” In this article we develop a latent variable model to characterize…

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临床试验设计中的贝叶斯方法与伦理AI 解读

Partial table of contents: MAJOR ISSUES Ethically Optimizing Clinical Trials (K. Schaffner) Admissibility of Treatment (N. Sedransk) TEST CASE: VERAPAMIL/NITROPRUSSIDE The Mechanics of Conducting a Clinical Trial (E. Heitmiller & T. Blanck) Issues of Statistical Design (N. Sedransk) Operational History and Procedural Feasibility (J. Kadane) Verapamil versus Nitroprusside: Results of the Clinical Trial I (J. Kadane & N. Sedransk) Verapamil versus Nitroprusside: Results of the…

使两个或多个抽样调查中共同变量的估计保持一致AI 解读

In practice, for many sample surveys the estimates of several population totals are based on one set of weights, which reproduces the known population totals of auxiliary variables. Such a set can always be obtained by using the general regression estimator. If some variables, not necessarily with known population totals, are jointly collected in two sample surveys, then it may be desirable that the weights of both surveys produce the same estimates for the unknown…

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大西洋鳕鱼种群年龄组成的序约束贝叶斯估计AI 解读

The management of a commercial fishery often requires estimates of the age composition. These estimates are typically based on age and length data obtained from sampling the commercial landings from the fishery and the catches from a research vessel survey. We use data from annual research cruises of Georges Bank conducted by the Canadian Department of Fisheries and Oceans to show how inferences for Atlantic cod (Gadus morhua) can be improved. Traditionally, two-phase…

空间疾病发生率的回归方法：估计函数途径AI 解读

Epidemiologists commonly study the geographical variation of disease rates to generate and refine testable hypotheses regarding etiology. Poisson regression is often used to estimate the parameters that characterize the effects of risk factors on disease. Hierarchical models have been proposed to utilize spatial locations and neighbors as surrogates for unknown or unmeasured risk factors in the analysis of disease rates. Although hierarchical models are useful in modeling…

基于特征值分解的正则化高斯判别分析AI 解读

Friedman proposed a regularization technique (RDA) of discriminant analysis in the Gaussian framework. RDA uses two regularization parameters to design an intermediate classifier between the linear, the quadratic the nearest-means classifiers. In this article we propose an alternative approach, called EDDA, that is based on the reparameterization of the covariance matrix [Σ k ] of a group Gk in terms of its eigenvalue decomposition Σ k = λ k D k A k D k ′, where λk specifies…

多个独立群体中的共同典型变量AI 解读

Suppose that data are collected from k independent but closely related populations and that a canonical correlation analysis is to be performed within each group. In such a situation, it may turn out that the transformation to canonical variates is similar across all k groups. The common canonical variates model studied in this article assumes that the transformation to canonical variates is actually identical across groups, while the canonical correlations may vary. We…

存在干扰参数时的检验AI 解读

We are interested in testing Ψ = 0 against an alternative in the presence of some nuisance parameter λ. The usual procedure for such problems is to use a test statistic that is a function of the data only. Let q(λ) denote the p-value at a given value λ. If q(λ) does not depend on λ, then in principle we can apply this procedure. However, a major difficulty that arises in many situations is that q(λ) depends on λ and therefore cannot be used as a p-value. In such cases, the…

多个总体随机序关系的似然比检验AI 解读

The likelihood ratio test is often used to test hypotheses involving a stochastic ordering. Distribution theory for the likelihood ratio test has been developed only for two stochastically ordered distributions. For testing equality of distributions against a stochastic ordering in several populations, this paper derives the null asymptotic distribution of the likelihood ratio test statistic, which is characterized by minimization problems and has no closed form. A Monte…

正态得分、正态概率图与正态性检验AI 解读

In this article we develop new plotting positions for normal plots. The use of the plots usually centers on detecting irregular tail behavior or outliers. Along with the normal plot, we develop tests for various departures from normality, especially for skewness and heavy tails. The tests can be considered as components of a Shapiro-Wilk type test that has been decomposed into different sources of nonnormality. Convergence to the limiting distributions is slow, so finite…