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参数密度估计中的一致性原则AI 解读

In parametric density estimation the existence of a prior distribution on the parameter dictates the use of the corresponding predictive density function as estimate. This paper argues that in a decision theory approach to parameter density estimation any loss function introduced should lead to this predictive result for situations where prior information is available. The KullbackLeibler directed divergence has this coherence property whereas the corresponding symmetric…

In parametric density estimation the existence of a prior distribution on the parameter dictates the use of the corresponding predictive density function as estimate. This paper argues that in a decision theory approach to parameter density estimation any loss function introduced should lead to this predictive result for situations where prior information is available. The KullbackLeibler directed divergence has this coherence property whereas the corresponding symmetric…

组成数据的主成分分析AI 解读

Compositional data, consisting of vectors of proportions, have proved difficult to handle statistically because of the awkward constraint that the components of each vector must sum to unity. Moreover such data sets frequently display marked curvature so that linear techniques such as standard principal component analysis are likely to prove inadequate. From a critical reexamination of previous approaches we evolve, through adaptation of recently introduced transformation…

组成数据的统计分析AI 解读

Summary The simplex plays an important role as sample space in many practical situations where compositional data, in the form of proportions of some whole, require interpretation. It is argued that the statistical analysis of such data has proved difficult because of a lack both of concepts of independence and of rich enough parametric classes of distributions in the simplex. A variety of independence hypotheses are introduced and interrelated, and new classes of…

核方法在多元二元数据判别中的应用AI 解读

An extension of the kernel method of density estimation from continuous to multivariate binary spaces is described. Its simple nonparametric nature together with its consistency properties make it an attractive tool in discrimination problems, with some advantages over already proposed parametric counterparts. The method is illustrated by an application to a particular medical diagnostic problem. Simple extensions of the method to categorical data and to data of mixed binary…

基于核方法的多元二元数据判别AI 解读

An extension of the kernel method of density estimation from continuous to multivariate binary spaces is described. Its simple nonparametric nature together with its consistency properties make it an attractive tool in discrimination problems, with some advantages over already proposed parametric counterparts. The method is illustrated by an application to a particular medical diagnostic problem. Simple extensions of the method to categorical data and to data of mixed binary…

线性损失下位置与尺度参数的区间估计AI 解读

A decision-theory approach to the estimation, by interval or point, of location and scale parameters based on a piecewise-linear loss function is presented. Of particular interest is the simple relationship of the equivalent confidence coefficient of the emerging interval estimators to the constants of the loss function.

位置与尺度参数的线性损失区间估计AI 解读

Estimation, in both theory and practice, tends to be divided into two almost distinct branches. On the one hand, point estimation, by providing a working value for the unknown true parameter value, is undoubtedly useful in further investigations of the given situation although its reliability may be difficult to assess in real terms through the medium of the estimated standard error. On the other hand, confidence interval estimation, by presenting a whole set of more or less…

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统计预测中的若干问题AI 解读

SUMMARY A general framework is introduced for the study of inference and decision predictions about the outcome of a future experiment from the data of an independent informative experiment. This allows a simple classification of prediction problems, and shows the place of standard inference predictions within the framework. A Bayesian approach to decision prediction is then presented and techniques appropriate to a variety of realistic utility functions are developed.…

似然比检验与置信域检验AI 解读

Summary A previous paper (Aitchison, 1964) proposed a method of confidence-region testing for multiple-hypothesis situations and developed the theory for linear univariate situations and for the asymptotic parametric case. The present paper shows that the results for these situations are in fact special cases of a basic relation between confidence-region tests and likelihood-ratio tests. This relation allows the easy extension of confidence-region testing to multivariate…

置信区域检验AI 解读

Summary To test a hypothesis that a parameter has value θ* we usually ask whether an observation falls in a critical region of the outcome space. It is well known that, by a suitable choice of confidence region, an equivalent test is to ask whether θ* lies outside the confidence region. In this paper the concept of such a confidence-region test is extended in directions which are relevant to the study of data-snooping and multiple-hypothesis testing. These problems are…

预测问题中贝叶斯与频率学派方法的比较：贝叶斯容忍域AI 解读

Summary In the theory of statistical tolerance regions, as usually presented in frequentist terms, there are inherent difficulties of formulation, development and interpretation. The present paper re-examines the basic problem from a Bayesian point of view and suggests that such an approach provides a set of widely applicable, mathematically tractable tools, often more tailored to the requirements of users than the corresponding frequentist tools. For the one-dimensional…

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最大似然估计程序及其配套显著性检验AI 解读

Summary The essence of many statistical problems, including most standard techniques, is to test whether or not the unknown parameters of an appropriate statistical model satisfy certain restrictions; and the outcome of such a test dictates whether it is necessary to provide estimates of these parameters which also satisfy the restrictions. In this paper we discuss and illustrate the relative merits, as practical tools for the consulting statistician, of two large-sample…

余料的统计理论AI 解读

SUMMARY In certain manufacturing processes where varying lengths of material are produced and subsequently cut up into unit lengths the problem of loss from wasted material arises. In this paper we postulate a statistical model of such a process and study how and in what sense we may minimize this loss. Two simple tests of whether a process is under optimum control are proposed. Finally we consider briefly two extensions of the theory to corresponding problems in k…

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