摘要:

Several classes of efficiency-robust linear unbiased estimators of location based on k sample quantiles are defined. The efficiencies of these estimators under the normal, logistic, and double exponential distributions are computed for sample sizes n = 20, 30, 40, 50, 100, ∞, and subsamples of size k = 2, 6, 10, 20. These results are then discussed in relation to other research in efficiency-robust estimation.

ISSN:0162-1459    

DOI:10.1080/01621459.1971.10482313

出版商:Taylor & Francis Group    

年代:1971

数据来源: Taylor

摘要:

Exact expectations and variances have been obtained for the maximum likelihood estimates of the elements of the mean vector and covariance matrix of the multivariate normal distribution when a subset of the variates does not have observations on some sampling units. The biases, variances, and mean square errors of the estimates are compared with those of the usual estimates computed from the complete observation vectors. When the correlations between the complete and incomplete sets of variates are small the multivariate missing value estimates are less efficient in the mean square error sense.

ISSN:0162-1459    

DOI:10.1080/01621459.1971.10482314

出版商:Taylor & Francis Group    

年代:1971

数据来源: Taylor

摘要:

The probabilities of the Type I errors of the Welch approximate-t test and the Aspin-Welch test for the Behrens-Fisher problem have been calculated for selected sets of degrees of freedom and nominal significance levels. The results show satisfactory agreement to the desired level. Thus, in practice, one can just use the usual t-table to carry out the Welch approximate t-test without much loss of accuracy.

ISSN:0162-1459    

DOI:10.1080/01621459.1971.10482315

出版商:Taylor & Francis Group    

年代:1971

数据来源: Taylor

摘要:

X1X2, ···, Xk1, Y1, Y2, ···, Yk2are k1+ k2mutually independent Poisson random variables with parameters λ1, λ2, ···, λk1, μ1, μ2, ···, μk2, respectively. Confidence intervals and tests of hypotheses for the parameter θ = λ1λ2··· λk1/ μ1μ2··· μk2are obtained. Under suitable conditions these procedures may be used to obtain approximate confidence intervals and tests of hypotheses of the parameter ρ = ρ1ρ2··· ρk1/ρk1+1ρk1+2··· ρk1+k2, where the ρi's, i = 1, 2, ···, k1+ k2are binomial parameters. This problem is of importance in reliability analysis and some applications to reliability analysis are exhibited.

ISSN:0162-1459    

DOI:10.1080/01621459.1971.10482316

出版商:Taylor & Francis Group    

年代:1971

数据来源: Taylor

摘要:

The main problem to be solved here may be described as follows: Let X1, X2, ··· be independent random variables, each with density fθ(x) = 1/θ over (0, θ) and zero elsewhere. It is desired to estimate the unknown parameter θ by an interval of length at most d units and with confidence at least 1 −α, for some specified d>0 and α in (0, 1). An exact solution and an asymptotic theory for a sequential procedure are given in Sections 1 and 2, respectively. The procedure proposed in this article satisfies an admissibility criterion which may be stated in terms of the maximum possible number of observations or, alternatively, the expected number of observations.

ISSN:0162-1459    

DOI:10.1080/01621459.1971.10482317

出版商:Taylor & Francis Group    

年代:1971

数据来源: Taylor

摘要:

The selection of experimental arrangements with resource constraints is structured as a mathematical optimization problem: maximize experimental efficiency subject to resource constraints, maintaining an integer number of observations in each cell. Three previously published measures of efficiency are examined. It is shown that the resulting integer programs can be solved using a variation on the Lawler-Bell algorithm. Eleven examples with up to 82 binary variables are solved. These examples illustrate that the measures of efficiency are inconsistent. One, due to Wald, is recommended as superior on numerical grounds.

ISSN:0162-1459    

DOI:10.1080/01621459.1971.10482318

出版商:Taylor & Francis Group    

年代:1971

数据来源: Taylor

摘要:

Cluster analysis involves the problem of optimal partitioning of a given set of entities into a pre-assigned number of mutually exclusive and exhaustive clusters. Here the problem is formulated in two different ways with the distance function (a) of minimizing the within groups sums of squares and (b) minimizing the maximum distance within groups. These lead to different kinds of linear and non-linear (0–1) integer programming problems. Computational difficulties are discussed and efficient algorithms are provided for some special cases.

ISSN:0162-1459    

DOI:10.1080/01621459.1971.10482319

出版商:Taylor & Francis Group    

年代:1971

数据来源: Taylor

摘要:

In their article [1] B. G. Greenberg, et al. discussed Simmons' modification of Warner's Randomized Response Technique and advised on the choice of the parameters in the model. One of their recommendations, however, is far from being the most efficient. The correctness of their other recommendations is proved and it is shown that the optimized method is superior to Warner's Technique.

ISSN:0162-1459    

DOI:10.1080/01621459.1971.10482320

出版商:Taylor & Francis Group    

年代:1971

数据来源: Taylor

摘要:

A conditional likelihood ratio test for testing a hypothesis concerning structural parameters in the presence of infinitely many incidental parameters is suggested. It is shown that the usual X2approximation to the log-likelihood ratio fails to work in many situations involving incidental parameters. In contrast it is shown that the X2approximation can be used in large samples under fairly general assumptions if we use conditional likelihood ratio tests instead. The relationship between the theory of UMPU-test and conditional likelihood ratio tests is discussed, and some examples are given to show that the conditional likelihood ratio approach covers more cases than the UMPU approach.

ISSN:0162-1459    

DOI:10.1080/01621459.1971.10482321

出版商:Taylor & Francis Group    

年代:1971

数据来源: Taylor

摘要:

The maximum likelihood estimate of the difference of the means is obtained in sampling from a bivariate normal distribution with unknown variances and co-variance when some of the observations on one of the variables are missing. This estimate is compared to several others by using the mean square error criterion. It is found that, when there are a moderate number of complete pairs of observations, the maximum likelihood estimate has the smallest mean square error for most of the parameter values. Illustrative tables are given to support our conclusions.

ISSN:0162-1459    

DOI:10.1080/01621459.1971.10482322

出版商:Taylor & Francis Group    

年代:1971

数据来源: Taylor