摘要:

The personalistic theory of probability prescribes that a person should use personal probability assessments in decision-making and that these assessments should correspond with his judgments. Since the judgments exist solely in the assessor's mind, there is no way to prove whether or not this requirement is satisfied. De Finetti has proposed the development of methods which should oblige the assessor to make his assessments correspond with his judgments. An ideal Assessor is hypothesized and his behavior is investigated under a number of such methods (including those suggested by de Finetti and others). The implications of these methods for the theory of personal probability are discussed. Finally, although the present interest is primarily normative, the practicability of the methods is also discussed.

ISSN:0162-1459    

DOI:10.1080/01621459.1967.10500920

出版商:Taylor & Francis Group    

年代:1967

数据来源: Taylor

摘要:

The designing of some multi-factor “analytical” studies of survey data is considered in this paper. It is assumed that, for each factor, there are two categories of interest and these are to be compared. The main objective is to allocate the sample so that the desired precision for the specified contrasts is obtained at minimum cost. It is assumed that one may sample independently in each of the sub-populations under investigation.

ISSN:0162-1459    

DOI:10.1080/01621459.1967.10500921

出版商:Taylor & Francis Group    

年代:1967

数据来源: Taylor

摘要:

Suppose given a set of similarities (or dissimilarities) between pairs of of objects from some set of objects, such as animal species, books, colours. We wish to construct from this similarity matrix a tree, or nested set of clusterings of the objects; graphs of trees provide a striking visual display of similarity groupings of the objects. The construction requires (1) a definition specifying when a similarity matrix has exact tree structure, (2) a measure of distance between any two similarity matrices, which yields (when combined with (1)) a measure of distance between any similarity matrix and any tree, (3) a family of local operations on a tree, which can be used to search out trees which best fit a given similarity matrix. The construction technique is applied to voting behaviour of the 50 United States in the last 13 presidential elections, giving a tree clustering of the states.

ISSN:0162-1459    

DOI:10.1080/01621459.1967.10500922

出版商:Taylor & Francis Group    

年代:1967

数据来源: Taylor

摘要:

This paper deals with methods of “cluster analysis”. In particular we attack the problem of exploring the structure of multivariate data in search of “clusters”.

ISSN:0162-1459    

DOI:10.1080/01621459.1967.10500923

出版商:Taylor & Francis Group    

年代:1967

数据来源: Taylor

摘要:

LetTjbe a reasonable estimator (for example, a minimum mean square error estimator) of the parameter θ of the familyDjof distributions,j= 1, 2, …,m.An estimatorT, which is a weighted mean ofT1,Ts, …,Tm, is found that has the same asymptotic distribution as that ofTj, when the sample comes fromDj,j= 1, 2, …,m.Here the weights are functions of the sample items. Empirical evidence is given which indicates thatTis satisfactory for small sample sizes. It is proved that ifTjand the weightWjare odd location and even location-free statistics, respectively,j= 1, 2, …,m, thenT= ΣWiTi, where ΣWi= 1, is an unbiased estimator of the center of every symmetric distribution, provided certain expectations exist. This is useful in the construction of the weight functionWj.

ISSN:0162-1459    

DOI:10.1080/01621459.1967.10500924

出版商:Taylor & Francis Group    

年代:1967

数据来源: Taylor

摘要:

Various methods are discussed for the problem of comparing two or more populations with respect to a response variableYin the presence of a (possibly multivariate) concomitant variableX—a situation in which the usual method is the standard one-way analysis of covariance. A method based on ranks is developed.

ISSN:0162-1459    

DOI:10.1080/01621459.1967.10500925

出版商:Taylor & Francis Group    

年代:1967

数据来源: Taylor

摘要:

A class of permutation tests based on appropriateU-statistics is proposed for the multisample location, scale, and association problems. TheseU-statistics need not be functions solely of the ranks of the different sample observations and for the application of the tests the parent distributions need not be continuous. The proposed tests are based on the existence of some equally likely permutations of the sample observations and are valid for small as well as large sample sizes. Further, the underlying permutation principle yields optimum estimators of the variances and covariances ofU-statistics entering into the expressions for the test statistics. The large sample test procedure is thereby simplified. This paper consists partly of expository material and partly of extensions of some allied two-sample results, considered earlier by the author (Sen [28]).

ISSN:0162-1459    

DOI:10.1080/01621459.1967.10500926

出版商:Taylor & Francis Group    

年代:1967

数据来源: Taylor

摘要:

Some optimum nonparametric procedures for estimating and testing contrasts in two-way layouts are proposed and studied. These procedures are based on the Chernoff-Savage [4] type of rank order statistics which include the Wilcoxon and normal scores statistics among others. In the first three sections, the properties of the proposed point estimators of contrasts, such as symmetry, invariance and asymptotic normality, are studied and their asymptotic relative efficiencies with respect to the corresponding least-squares estimators are obtained. In particular, it is shown that the procedures based on the normal scores statistics are asymptotically at least as efficient as the corresponding procedures based on the method of least squares, whatever be parent cumulative distribution functions. In sections 4 and 5, the corresponding problems of testing and confidence intervals are discussed, and generalized to two-way layouts with several observations per cell.

ISSN:0162-1459    

DOI:10.1080/01621459.1967.10500927

出版商:Taylor & Francis Group    

年代:1967

数据来源: Taylor

摘要:

A general method of determining efficiency-robust estimation and testing methods is presented. This is used to deriveadmissible linear unbiased estimators(ALUEs) having the following optimality property: Over a specified (finite) family of possible symmetric shapes of the error distribution, the estimator's respective variances cannot be jointly improved. Such estimators are generalizations of Lloyd's best linear unbiased estimators (BLUEs) determined for single shapes. Simple illustrative examples are given. Other applications of the method to estimation and testing problems are discussed briefly.

ISSN:0162-1459    

DOI:10.1080/01621459.1967.10500928

出版商:Taylor & Francis Group    

年代:1967

数据来源: Taylor

摘要:

In the classical two sample problem, the null hypothesis of identical distribution functions is tested. Rank testing procedures have the property that they are valid (have Type I error identically equal to α) for any absolutely continuous distribution function. Choices among rank tests are usually based upon local power calculations for a given specified null distribution against specific parametric alternatives. A rank test is said to be efficiency robust when no other has a uniformly better local power performance (risk point) for a specified class A of distribution function alternativesF.Such rank tests may be constructed using formal Bayes procedures resulting in convex mixtures of the locally most powerful rank testsTFforFεΛ. Asymptotic relative efficiency (ARE) calculations uncover the symmetry relation ARE (TF, TF*;F) = ARE (TF*,TF; F*). Examples involving Logistic, Normal and Double Exponential are considered.

ISSN:0162-1459    

DOI:10.1080/01621459.1967.10500929

出版商:Taylor & Francis Group    

年代:1967

数据来源: Taylor