ISSN:0162-1459    

DOI:10.1080/01621459.1967.10482883

出版商:Taylor & Francis Group    

年代:1967

数据来源: Taylor

摘要:

We define and evaluate some simple estimators of the linear regression function ofyandx, when observations may be missing onyorx.In particular, we compare the zero order estimator, a modified zero order estimator, and mixed estimators relative to the least squares estimator using the ratio of expected mean square errors as our measure of efficiency. Illustrative tables are given to support our conclusions regarding the estimator of choice.

ISSN:0162-1459    

DOI:10.1080/01621459.1967.10482884

出版商:Taylor & Francis Group    

年代:1967

数据来源: Taylor

摘要:

A number of multivariate exponential distributions are known, but they have not been obtained by methods that shed light on their applicability. This paper presents some meaningful derivations of a multivariate exponential distribution that serves to indicate conditions under which the distribution is appropriate. Two of these derivations are based on “shock models,” and one is based on the requirement that residual life is independent of age. It is significant that the derivations all lead to the same distribution.

ISSN:0162-1459    

DOI:10.1080/01621459.1967.10482885

出版商:Taylor & Francis Group    

年代:1967

数据来源: Taylor

摘要:

Some similar items are to be independently life-tested under “typical” conditions. The interest is in predetermining a length of time such that the probability is at least a specified amount that an item will survive this long. A random lower bound for this time is to be evaluated from preliminary independent life-tests on a few items, combined with supplementary information. The time to failure for an item is assumed to have a lognormal distribution. The testing conditions are the same for the items to be life-tested later. However, the few items tested first might be subjected to different conditions. A consensus of these conditions furnishes the “typical” conditions. The few observations are used to allow for mean effects, and an upper bound (perhaps rough) for the variation effects is provided by the supplementary information. The resulting bounds can have strong advantages over use of at-statistic when only two or three items are considered initially.

ISSN:0162-1459    

DOI:10.1080/01621459.1967.10482886

出版商:Taylor & Francis Group    

年代:1967

数据来源: Taylor

摘要:

Bayesian analysis of the exponential model, based on life tests that are terminated at preassigned time points or after preassigned number of failures, has been developed. For the prior distribution of the parameter involved, uniform, inverted gamma and exponential densities have been examined. The estimation of the reliability function has also been carried out by using Bayesian methods and the case of ‘attribute testing’ has been considered briefly. The role of prior quasi-densities when a life tester has no prior information has been illustrated and it has been observed that the reliability estimate for a diffuse prior which is uniform over the entire positive real line closely resembles the classical MVU estimate obtained by Pugh. It has also been noted that the Bayes estimate of the exponential parameter θ for a prior quasi-density of the form 1/θ2coincides with the classical MVU estimate of Epstein and Sobel. Further, it has been proved that in a wide class of prior densities, proper or improper, 1/θ2is the only prior which leads to the MVU estimate.

ISSN:0162-1459    

DOI:10.1080/01621459.1967.10482887

出版商:Taylor & Francis Group    

年代:1967

数据来源: Taylor

摘要:

Discussed here are several aspects of a simple model for dealing with nonresponse. The model is, in a sense, a sequential one and is developed from a Bayesian decision theory point of view. Within this framework we examine how formalization and combination of one's opinions, past experience, and “objective” evidence concerning the proportion of non-respondents, the differences and relations between respondents and nonrespondents, the cost of obtaining information from nonrespondents, etc., might influence optimal decisions concerning the sampling of nonrespondents. The influence of nonresponse on the overall optimal sample design is also discussed, as well as several generalizations of the basic model, to handle a hard core of nonresponse.

ISSN:0162-1459    

DOI:10.1080/01621459.1967.10482888

出版商:Taylor & Francis Group    

年代:1967

数据来源: Taylor

摘要:

In 1963 Fellegi proposed a new method of sampling without replacement with probability proportional to size, which allowed for rotation of the sample (within certain limits) simultaneously with the exact calculation of joint probabilities of selection of sets of units. Fellegi was able to show that for samples of size two units his equations always yielded a solution, provided that the largest of the population units did not exceed one third of the size of the whole population. He also indicated that the method would probably work provided the largest unit was less than one half the size of the whole population, and that a proof of this would be desirable. This note supplies geometrical proofs of the existence and uniqueness of the solution to Fellegi's equations given this condition.

ISSN:0162-1459    

DOI:10.1080/01621459.1967.10482889

出版商:Taylor & Francis Group    

年代:1967

数据来源: Taylor

摘要:

A simple step-wise procedure for the clustering of variables is described. Two alternative criteria for the merger of groups at each pass are discussed: (1) maximization of the pairwise correlation between the centroids of two groups, and (2) minimization of Wilks’ statistic to test the hypothesis of independence between two groups. For a set of sample covariance matrices the step-wise solution for each criterion is compared with the optimal two-group separation of variables found by total enumeration of the possible groupings.

ISSN:0162-1459    

DOI:10.1080/01621459.1967.10482890

出版商:Taylor & Francis Group    

年代:1967

数据来源: Taylor

ISSN:0162-1459    

DOI:10.1080/01621459.1967.10482891

出版商:Taylor & Francis Group    

年代:1967

数据来源: Taylor

摘要:

This paper is devoted to a discussion of an iterative procedure for obtaining the maximum likelihood estimator of the covariance matrix for multivariate experiments in which measurements on certain components of a normal vector random variable are intentionally omitted in corresponding subgroups of the experimental units. The proposed algorithm, which is based on the Newton-Raphson method, is outlined in detail in Section 5. A special design is included to illustrate the procedure and a few areas of application are indicated.

ISSN:0162-1459    

DOI:10.1080/01621459.1967.10482892

出版商:Taylor & Francis Group    

年代:1967

数据来源: Taylor