摘要:

When sampling from a multinomial population, it may happen either by chance or by design that some of the observations are only partially classified. In this article the amount of information in the partially classified observation is evaluated, and maximum likelihood estimators are obtained using both completely classified and partially classified data. In general an iterative solution is required, but special cases are identified in which the solution is obtained in closed form.

ISSN:0162-1459    

DOI:10.1080/01621459.1971.10482220

出版商:Taylor & Francis Group    

年代:1971

数据来源: Taylor

摘要:

In this article, an alternative v for the vector û of least-squares residuals in the linear model is derived. It is best in the class of all linear unbiased estimators' of u having a certain fixed covariance matrix chosen a priori. Under the normality assumption, the distribution of the Von Neumann Ratio based on v is independent of the regression vectors, so that v is particularly useful for testing on serial correlation of the disturbances. It is pointed out that the existing tests for serial correlation in economic time-series models might be improved by using v based on an appropriate covariance matrix; the Durbin-Watson upper-bound tables can be used for this purpose.

ISSN:0162-1459    

DOI:10.1080/01621459.1971.10482221

出版商:Taylor & Francis Group    

年代:1971

数据来源: Taylor

摘要:

A two-stage estimate for the mean vector of a multivariate distribution is proposed for the situation in which the prior knowledge about the mean vector can be expressed in the form of an initial estimate. The proposed estimate is compared with the sample mean based on a single sample of equivalent size. The proposed estimate is also compared with the Bayes' estimate based on an equivalent sample. The latter comparison has been accomplished only for the univariate case.

ISSN:0162-1459    

DOI:10.1080/01621459.1971.10482222

出版商:Taylor & Francis Group    

年代:1971

数据来源: Taylor

摘要:

An experimenter has a sample for estimating the variance σ32. Suppose he has two other independent samples which are suspected to have come from the same population with variance σ32. Whether to pool the three samples to estimate σ32depends on the outcome of two preliminary tests. This article discusses a sometimes pool estimate of σ32and compares this with the usual estimate of σ32, obtained from the first sample only, as regards bias and mean square error.

ISSN:0162-1459    

DOI:10.1080/01621459.1971.10482223

出版商:Taylor & Francis Group    

年代:1971

数据来源: Taylor

摘要:

are proposed for the cases of Normal, Gamma, Poisson, and Binomial distributions. The behavior of these estimators is compared with that of the ones suggested by Thompson [3]. Our estimators are shown to be better in the sense of having a smaller mean square error in an interval around μ0.

ISSN:0162-1459    

DOI:10.1080/01621459.1971.10482224

出版商:Taylor & Francis Group    

年代:1971

数据来源: Taylor

摘要:

It is frequently necessary to combine the information provided by summary statistics for different observation sets, particularly in the context of group decision processes. Problems arise when there are unidentified observations that overlap, that is, belong to more than one set. This article discusses the handling of these problems in relation to a Normal example when the exact extent of overlap is known.

ISSN:0162-1459    

DOI:10.1080/01621459.1971.10482225

出版商:Taylor & Francis Group    

年代:1971

数据来源: Taylor

摘要:

The purpose of this article is to suggest a method of estimating parameters of linear regressions containing two independent variables, when data is missing among these variables. The problem envisaged concerns the case where: (1) the independent variables are considered as fixed numbers; (2) each observation contains the values of the dependent variable and at least one of the independent variables; (3) some observations are complete. In contrast with other approaches dealing with similar problems, the technique developed in this article has the following advantages: (1) it is based on rather unrestrictive hypotheses; (2) the resulting estimators are consistent; (3) the asymptotic variances of these estimators are smaller than those of comparable estimators described in the literature. Although the question is not examined in the present article, if seems also that the proposed method offers good possibilities of generalization.

ISSN:0162-1459    

DOI:10.1080/01621459.1971.10482226

出版商:Taylor & Francis Group    

年代:1971

数据来源: Taylor

摘要:

This article considers the problem of adjusting monthly or quarterly time series to make them accord with independent annual totals or averages without introducing artificial discontinuities. A general approach and some specific procedures involving constrained minimization of a quadratic form in the differences between revised and unrevised series are proposed. Some computational advantages are noted. Attention is given to the relationships between the adjustment problem and earlier work by other authors on the creation of monthly or quarterly series when only annual figures are available. An example is provided to illustrate the application of the proposed adjustment procedures.

ISSN:0162-1459    

DOI:10.1080/01621459.1971.10482227

出版商:Taylor & Francis Group    

年代:1971

数据来源: Taylor

摘要:

In this article bivariate failure rate is defined, and it is shown that no absolutely continuous bivariate distribution with constant failure rate exists except in the special case when the marginals are independently distributed.

ISSN:0162-1459    

DOI:10.1080/01621459.1971.10482228

出版商:Taylor & Francis Group    

年代:1971

数据来源: Taylor

摘要:

Naus [2] derived the moment generating function of the logarithm of the sum of two variates whose logarithms are independent normal variates with equal variances. The present article generalizes the results of Naus to the case when the logarithms of the variates have a bivariate normal distribution with unequal variances and correlation coefficient ρ.

ISSN:0162-1459    

DOI:10.1080/01621459.1971.10482229

出版商:Taylor & Francis Group    

年代:1971

数据来源: Taylor