摘要:

This note presents a simple proof that the Horvitz-Thompson estimator

ISSN:0162-1459    

DOI:10.1080/01621459.1969.10501061

出版商:Taylor & Francis Group    

年代:1969

数据来源: Taylor

摘要:

Conditions are presented under which inalllinear models with a common specified systematic part every linear simple least squares estimator is also best. The behaviour of mean squares and test ratios in ordinary analysis of variance tables under these and also less stringent conditions is discussed with illustrative examples given.

ISSN:0162-1459    

DOI:10.1080/01621459.1969.10501062

出版商:Taylor & Francis Group    

年代:1969

数据来源: Taylor

摘要:

General results are obtained for an approximation to the variance of a weighted regression estimator in which the weights are sample estimators of unknown unpatterned variances. Independent normally distributed errors are specified for the linear response model used in the development. Applications to four examples of weighted sample means and linear regression in a single factor are studied. The most important practical conclusion drawn from the results of these examples is that each estimated weight should be based on at least ten degree of freedom.

ISSN:0162-1459    

DOI:10.1080/01621459.1969.10501063

出版商:Taylor & Francis Group    

年代:1969

数据来源: Taylor

摘要:

Various estimators of components of variance for the balanced one way layout are compared using mean squared error as a measure of performance. Several modifications of the maximum likelihood estimator and several formal Bayes estimators are compared and mean square error relationships are given. Inadmissibility is established for a large class of translation and scale invariant estimators. Numerical results are tabled and graphed to exhibit the relative efficiency of the estimators considered.

ISSN:0162-1459    

DOI:10.1080/01621459.1969.10501064

出版商:Taylor & Francis Group    

年代:1969

数据来源: Taylor

摘要:

This paper uses a family of bivariate extreme-value distributions to estimate the probability of a large exceedance of a random variable given that a certain other random variable not independent of the first has exceeded a certain value. A simple method of reasonably good efficiency is given for estimating a bivariate extreme-value distribution from independent bivariate samples. The method is used to analyze the performance of a spacecraft command receiver which has an indication of data quality so that commands likely to be in error can be rejected.

ISSN:0162-1459    

DOI:10.1080/01621459.1969.10501065

出版商:Taylor & Francis Group    

年代:1969

数据来源: Taylor

摘要:

The standard approach to the distribution of the number of runs appearing in a sequence is to make the result conditional on the number of each class of object which occurs. Illustrations are presented from the fields of psychology and zoology where invalid conclusions will be drawn under this assumption. By allowing the composition to fall at random, a multiple runs distribution is obtained which is conditional only on the total number of objects appearing in the sequence. Moments of the distribution are indicated along with an analysis of the normal approximation. Exact critical values for the number of runs in the case of two classes of objects are given so that a nonparametric test may be performed corresponding to the traditional runs test for randomness in an observed sequence.

ISSN:0162-1459    

DOI:10.1080/01621459.1969.10501066

出版商:Taylor & Francis Group    

年代:1969

数据来源: Taylor

摘要:

In this paper the first two moments of the Statistic (treatment sum of squares)/(treatment + error sums of squares) over all possible random assignments of treatments to the experimental plots are obtained for two associate PBIB designs. They are compared with the corresponding moments of a central beta distribution to study the extent to which the normal theory test may serve as an approximation to the randomization test. It is found that the approximation is reasonable for some classes of PBIB designs.

ISSN:0162-1459    

DOI:10.1080/01621459.1969.10501067

出版商:Taylor & Francis Group    

年代:1969

数据来源: Taylor

摘要:

The effect of relaxing the conditions regarding the equality of the mortality rates and of the errors of enumeration between the states and the nation, on the error in the estimation of the net migration rate by the census survival ratio method, is examined and it is shown that, when the national population is closed, the necessary and sufficient condition for this error to become zero is that the relative degree of enumeration for any agexof a given sex in theith state as compared with the degree of enumeration in the nation at the first census bears the same ratio to the relative degree of enumeration for the same cohort at age (x+n) at the second census, as the survival ratio of that cohort from agexto (x+n) in theith state bears to the corresponding survival ratio in the nation as a whole.

ISSN:0162-1459    

DOI:10.1080/01621459.1969.10501068

出版商:Taylor & Francis Group    

年代:1969

数据来源: Taylor

摘要:

For the general case of jointly distributed random variablesxandy, Goodman [3] derives the exact variance of the productxy.For the special case wherexandyare stochastically independent, he provides a simpler expression for the exact variance. We offer a weaker set of assumptions which suffices to yield the simpler expression. We then extend Goodman's analysis to present the exact covariance of two productsxyanduv, and sketch several specializations and applications.

ISSN:0162-1459    

DOI:10.1080/01621459.1969.10501069

出版商:Taylor & Francis Group    

年代:1969

数据来源: Taylor

摘要:

The sampling distribution of the range from a discrete uniform finite population is obtained. Its relation to the sampling distribution from a discrete uniform population is studied, and conditions under which one can approximate the other are given.

ISSN:0162-1459    

DOI:10.1080/01621459.1969.10501070

出版商:Taylor & Francis Group    

年代:1969

数据来源: Taylor