摘要:

Five biased estimators of the slope in straight line regression are considered. For each, the estimate of the “bias parameter”, k, is a function of N, the number of observations, and [rcirc]2, the square of the least squares estimate of the standardized slope, β. The estimators include that of Farebrother, the ridge estimator of Hoerl, Kennard, and Baldwin, Vinod's shrunken estimators., and a new modification of one of the latter. Properties of the estimators are studied for 13 combinations of N and 3. Results of simulation experiments provide empirical evidence concerning the values of means and variances of the biased estimators of the slope and estimates of the “bias parameter”, the mean square errors of the estimators, and the frequency of improvement relative to least squares. Adjustments to degrees of freedom in the biased regression analysis of variance table are also considered. An extension of the new modification to the case of p> 1 independent variables is presented in an Appendix.

ISSN:0361-0918    

DOI:10.1080/03610917808812095

出版商:Marcel Dekker, Inc.    

年代:1978

数据来源: Taylor

摘要:

A previous paper provided a locally optimal test statistic for combining s independent test statistics of a common multivariate hypothesis. Difficulty in calculating the critical values limited the applicability of the test. In this paper, it is shown that approximate critical values can be easily calculated, with negligible loss of accuracy for most situations.

ISSN:0361-0918    

DOI:10.1080/03610917808812096

出版商:Marcel Dekker, Inc.    

年代:1978

数据来源: Taylor

摘要:

In this paper, we restrict attention to the problem of subset selection of normal populations. The approaches and results of some previous comparison studies of subset selection procedures are discussed briefly. And then the result of a new Monte Carlo study comparing the performance of two classical procedures and the Bayes procedure is presented.

ISSN:0361-0918    

DOI:10.1080/03610917808812097

出版商:Marcel Dekker, Inc.    

年代:1978

数据来源: Taylor

摘要:

In the one-sample Student t-test, the occurrence of a type-I error is dependent on the estimates of the mean and standard deviation for a fixed sample size, n. The statistic can achieve significance either by the sample mean being too different from the hypothesized mean or by the sample standard deviation being too small. The critical region is partitioned to determine the characteristics of samples in the critical region, assuming the null hypothesis is true. As might be conjectured from the use of the t-statistic, mis-estimation of the mean is shown to be the predominant characteristic of samples in the critical region for sample sizes larger than 20 and significance level greater than 0.01. Underestimation of the variance, unless accompanied by a misestimation of the mean, is a far less frequent characteristic of critical region samples.

ISSN:0361-0918    

DOI:10.1080/03610917808812098

出版商:Marcel Dekker, Inc.    

年代:1978

数据来源: Taylor

摘要:

The power of Student's t-test is partitioned to determine* the proportion of time the sample standard deviation is too small or the mean is misestimated given that rejection of the hypothesis under test has occurred

ISSN:0361-0918    

DOI:10.1080/03610917808812099

出版商:Marcel Dekker, Inc.    

年代:1978

数据来源: Taylor