摘要:

AbstractThis paper gives an account of the collaboration between two mathematical statisticians and a toxicologist (the second author) interested in thin layer chromatography (TLC). A TLC “system” consists of a medium through which a solvent is transported. If a solution of some (toxic) sample is applied to the medium, then the components are carried forward by the solvent over different distances. Section 1 describes the concept of a data bank which provides standard values for the degrees of migration characteristic for each ofmwell‐studied substances in each ofnsystems. Sections 2–5 are mainly devoted to the construction of The “best design(s)”{j1*…jk*} ofksystems from thenavailable ones. The attention is restricted to the situation that an unidentified sample exclusively contains one of themsubstances covered by the data bank and produces the scoresxj…xjkin the systems j,…jkrespectively. Three different approaches to the identification problem were successively considered. Each approach leads to a class of procedures and their performances. The performance of the optimum procedure can be used to define the performance of any of the (nk) designs (j1…jk}. The latter performance is maximized in order to determine {j1*.,.,jk*}. In practice usually data is obtained for mixtures instead of single. pure substances. Section 6 gives some tentative theory for the eval

ISSN:0039-0402    

DOI:10.1111/j.1467-9574.1980.tb00700.x

出版商:Blackwell Publishing Ltd    

年代:1980

数据来源: WILEY

摘要:

SummaryThis paper describes the small and moderate sample behaviour of three studentized non‐parametric statistics by Sen and a modified Wilcoxon statistic by Potthoff for testing the equality of location parameters in the presence of dispersion differences. Based on the agreement between the asymptotic and small sample distributions of the statistics as well as a comparison of their power under heteroscedasticity, the studentized Wilcoxon and the studentized Brown and Mood tests arc preferred in the two‐sample and c‐sample situations, respect

ISSN:0039-0402    

DOI:10.1111/j.1467-9574.1980.tb00701.x

出版商:Blackwell Publishing Ltd    

年代:1980

数据来源: WILEY

摘要:

SummaryIn empirical Bayes decision making, the Bayes empirical Bayes approach is diccussed by Gilliland and Boyer (1979). In the finite state component case, the Bayes empirical Bayes procedures are shown to have optimal properties in a fairly general setting and believed to have small sample advantage over the classical rules. The flexibility of making desirable adjustments for these decision procedures by choice of prior enables one to set a proper strategy when dealing with actual problems.The applications of Bayes empirical Bayes procedures, however, create some interesting theoretical and computational problems as they are fairly complicated in structure. This paper gives a brief introduction into the Bayes empirical Bayes approach, and, to illustrate it, explicit results are given for testing H0: N(‐1,1) against H1: N(1,1

ISSN:0039-0402    

DOI:10.1111/j.1467-9574.1980.tb00702.x

出版商:Blackwell Publishing Ltd    

年代:1980

数据来源: WILEY

摘要:

AbstractIn a paper by SrivenkataramanaTracy[4], four methods of estimating a population totalYwith the use of an auxiliary variable were introduced, given a random sample without replacement from that population. These methods were “built around the idea that estimating the population total is essentially equivalent to estimating the total corresponding to the non‐sample units, since that corresponding to the sample units is known once the sample is drawn and measurements are made on it.”However, in the case of small sampling fractions the nonsample units constitute most of the population and no great improvement over the traditional estimators is to be expected. Therefore the methods are compared with the existing estimators and it turns out that they are special cases of the “mixing estimators”, introduced in this paper. The latter estimators can be made asymptotically equivalent to the regression estimator and are therefore asymptotically superior to all other estimators. An exact comparison is carried out on the artificial example given in [4]. The statement in this paper that “the proposed estimators are to be preferred to the regression estimator for., superiority of performance in the case of small samples” is evidently misleading. Finally a comparison is made with other “mixing‐type” estimators, that can prove very

ISSN:0039-0402    

DOI:10.1111/j.1467-9574.1980.tb00703.x

出版商:Blackwell Publishing Ltd    

年代:1980

数据来源: WILEY

ISSN:0039-0402    

DOI:10.1111/j.1467-9574.1980.tb00704.x

出版商:Blackwell Publishing Ltd    

年代:1980

数据来源: WILEY

ISSN:0039-0402    

DOI:10.1111/j.1467-9574.1980.tb00705.x

出版商:Blackwell Publishing Ltd    

年代:1980

数据来源: WILEY

ISSN:0039-0402    

DOI:10.1111/j.1467-9574.1980.tb00706.x

出版商:Blackwell Publishing Ltd    

年代:1980

数据来源: WILEY