摘要:

The paper presents the results of an inquiry concerning the small sample relative efficiency of maximum likelihood and best unbiased estimators of reliability functions of one-unit systems. Three cases are considered: The Poisson, exponential, and normal (standard deviation known). Two kinds of relative efficiency functions are studied. The first kind consists of the common ratio of the Cramér-Rao lower bound of the variances of unbiased estimators, to the mean-square-error of the considered estimator. The second kind is a new type of a relative efficiency function, which is called ‘the closeness relative efficiency function.’ This function is defined as the ratio of the probabilities that the maximum likelihood and the best unbiased estimators yield estimates in a prescribed neighborhood of the unknown reliability value. A substantial part of the study is devoted to the derivation of the required moments of the estimators.

ISSN:0162-1459    

DOI:10.1080/01621459.1966.10482193

出版商:Taylor & Francis Group    

年代:1966

数据来源: Taylor

摘要:

The bias and mean-square-error functions of the maximum likelihood and best unbiased estimator of reliability functions are derived. Information is available on the operation of subsystems connected in series or in parallel. The Poisson and the exponential cases are considered.

ISSN:0162-1459    

DOI:10.1080/01621459.1966.10482194

出版商:Taylor & Francis Group    

年代:1966

数据来源: Taylor

ISSN:0162-1459    

DOI:10.1080/01621459.1966.10482195

出版商:Taylor & Francis Group    

年代:1966

数据来源: Taylor

ISSN:0162-1459    

DOI:10.1080/01621459.1966.10482196

出版商:Taylor & Francis Group    

年代:1966

数据来源: Taylor

摘要:

Comparisons of several populations with regard to their distributions on a qualitative attribute must often be based on sample data. An overall large sample test of homogeneity of all the populations is extended to provide multiple comparison tests on homogeneity of subsets of populations, and tests of partial homogeneity, i.e., homogeneity only on certain categories of the qualitative distributions. Grouping of populations into several homogeneous subsets can also be achieved by this procedure, and so can a similar grouping of categories. Probabilities of errors on various hypotheses and partial hypotheses are defined and computed. An alternative procedure is proposed which has some advantages.

ISSN:0162-1459    

DOI:10.1080/01621459.1966.10482197

出版商:Taylor & Francis Group    

年代:1966

数据来源: Taylor

摘要:

The overall least squares solution is found when a complete curve to be fitted consists of two or more submodels, and these have to be joined at points whose abscissae have to be estimated. Under certain standard conditions, each fitted submodel is itself a local least squares solution, and the overall least squares solution can be found quite easily.

ISSN:0162-1459    

DOI:10.1080/01621459.1966.10482198

出版商:Taylor & Francis Group    

年代:1966

数据来源: Taylor

摘要:

The “partial adjustment” and “adaptive expectations” models are simply special cases of a more general model. This fact has not been commonly recognized by investigators who have used one or the other of these two models in empirical economic research. An examination of the results of small sample experiments shows that the bias in the estimated regression coefficients and the estimated mean lag which occurs when either one of the models is fitted by least squares to data generated by the more general model is quite serious. Also it is found that the spread of the distribution of these estimates is very sensitive to this misspecification. The departures from normality of these distributions are notable for the smallest sample sizes examined, but perhaps less significant in view of the severity of the other problems noted.

ISSN:0162-1459    

DOI:10.1080/01621459.1966.10482199

出版商:Taylor & Francis Group    

年代:1966

数据来源: Taylor

摘要:

Two methods of construction of designs for two-way elimination of heterogeneity are given. The first method is based on the derived and residual designs of symmetrical balanced incomplete block designs. The second method utilises the balanced incomplete block design with parametersv= 2k, b= 2(2k− 1),r= 2k− 1 and λ =k− 1. It is further shown that the designs so constructed are either balanced or partially balanced.

ISSN:0162-1459    

DOI:10.1080/01621459.1966.10482200

出版商:Taylor & Francis Group    

年代:1966

数据来源: Taylor

摘要:

Small sample estimators are developed for two post strata and compared with pooling or collapsing procedures commonly employed in practice. The estimators are not necessarily conditionally unbiased for particular sample split, but their conditional M.S.E. may be smaller than that of the common post stratified estimator. It is proven that it is always possible to construct an estimator superior to the practice of combining two post strata when one contains few sample elements. A procedure for generalizing the two-strata procedures to any number of strata is illustrated. This procedure permits the construction of unbiased estimators for populations divided into a large number of small post strata.

ISSN:0162-1459    

DOI:10.1080/01621459.1966.10482201

出版商:Taylor & Francis Group    

年代:1966

数据来源: Taylor

摘要:

Let (X,Y) be bivariate normally distributed with mean (μ,v), var(X) = var(Y) = σ2, and correlation betweenXandYequal to ρ. Let (Xi,Yi) be independent observations on (X,Y) fori= 1, 2, · · ·,n. Because of practical considerations we observe onlyZi= min(Xi,Yi),i= 1, 2, · · ·,n. We are concerned with estimation and testing procedures when the parameter ρ is unknown. This model will be useful in certain studies of twins.

ISSN:0162-1459    

DOI:10.1080/01621459.1966.10482202

出版商:Taylor & Francis Group    

年代:1966

数据来源: Taylor