摘要:

This paper presents results, mainly in tabular form, of a sampling experiment in which 100 economic time series 25 years long were drawn at random from theHistorical Statistics for the United States. Sampling distributions of coefficients of correlation and autocorrelation were computed using these series, and their logarithms, with and without correction for linear trend. We find that the frequency distribution of autocorrelation coefficients has the following properties:

ISSN:0162-1459    

DOI:10.1080/01621459.1961.10480650

出版商:Taylor & Francis Group    

年代:1961

数据来源: Taylor

摘要:

Define the linear structural relation with parameters α, β, by μ = α +βv. This paper considers the problem of confidence region estimation of α and β based on a sample of independent pairs, (yi,xi),i= 1, 2, ···, withEyi= μi,Exi=vi. The pairs (yi,xi) are assumed to have a common (unknown) covariance matrix and to follow the bivariate normal distribution. Point estimates

ISSN:0162-1459    

DOI:10.1080/01621459.1961.10480651

出版商:Taylor & Francis Group    

年代:1961

数据来源: Taylor

摘要:

This note has as its primary purpose the correction of a statement made in a previous paper regarding the attainment of the variance of a proposed estimator of its lower bound. At the same time it seemed useful, as an expository function, to recapitulate a development of the lower bound which led this writer to a better understanding of it, and to the realization of the indicated error. Here the bound is developedab initiofrom a simple identity, instead of secondarily from Schwartz's inequality, as is usual. It should be stated that, mathematically, there is nothing essentially new in this development; however, it yields, in addition to a clarification of the “why” of the bound, a necessary, condition for its attainment. The element of novelty in the statement of this condition is doubtless mathematically trivial, but may be of use in application. Also it is hoped that its direct derivation from the same elementary identity as the bound itself is derived, may make it understood by the nonmathematician—and possibly even by mathematicians! The usual estimate of the mean of the normal function, whose variance is well known to attain the lower bound, is used as an example to illustrate how this condition is fulfilled, and the logistic function illustrates how it is not fulfilled.

ISSN:0162-1459    

DOI:10.1080/01621459.1961.10480652

出版商:Taylor & Francis Group    

年代:1961

数据来源: Taylor

摘要:

This paper describes a methodological study attempting to improve the quantitative analysis of migration data by controlling for seven important spatial variables. A primitive mathematical model is constructed by means of which theoretical migration frequencies are calculated and then compared with actual frequencies, yielding several indexes and a Force of Attraction. This approach was applied to United States internal migration for 1935–1940. The highest scores were obtained for the Pacific area. This model may be used for human, animal, or inanimate movements.

ISSN:0162-1459    

DOI:10.1080/01621459.1961.10480653

出版商:Taylor & Francis Group    

年代:1961

数据来源: Taylor

摘要:

The Mann-Whitney-Wilcoxon statistic is of some importance in non-parametric statistical inference. The asymptotic normality of this statistic has been established previously for the case where the distributions of the random variables, in each of the two samples, are the same. In the present work it is shown that this statistic is asymptotically normal when these distributions are not all the same. An application of this result to a particular hypothesis testing problem is also given.

ISSN:0162-1459    

DOI:10.1080/01621459.1961.10480654

出版商:Taylor & Francis Group    

年代:1961

数据来源: Taylor

摘要:

The iterative calculations required to obtain the maximum likelihood estimates of α and β in the distribution functiondF(z) =ez/(1 +ez)2dz, wherez= α +βx, are presented for doubly truncated, upper and lower truncated, and untruncated grouped samples. The calculations needed to obtain the maximum likelihood estimator of Pareto's constant are also given for a lower truncated grouped sample with both equal and unequal grouping. Asymptotic variances and covariances are derived for all estimators considered.

ISSN:0162-1459    

DOI:10.1080/01621459.1961.10480655

出版商:Taylor & Francis Group    

年代:1961

数据来源: Taylor

摘要:

Since a baseball game consists of a sequence of half-innings commencing in an identical manner, one is tempted to suppose that the progress of the score throughout a game would be well simulated by a sequence of random drawings from a single distribution of half-inning scores. On the other hand, the instincts of a baseball fan are offended at so simple a suggestion. The hypothesis is examined by detailed analysis of 782 professional games, and a supplementary analysis of a further 1000 games. It is shown that the scoring does vary significantly in the early innings, so that the same distribution cannot be used for each inning. But, with a few exceptions, total scores, establishments of leads, overcoming of leads, and duration of extra-inning games as observed in the actual games show good agreement with theoretical calculations based on random sampling of the half-inning scoring distributions observed.

ISSN:0162-1459    

DOI:10.1080/01621459.1961.10480656

出版商:Taylor & Francis Group    

年代:1961

数据来源: Taylor

摘要:

A method is described for solving by iteration the normal equations in multiple linear regression analysis when class differences are present, and a proof is given of the convergence of the process. Comparison is made with a direct method of solution in which the information matrix is adjusted for class differences before it is inverted.

ISSN:0162-1459    

DOI:10.1080/01621459.1961.10480657

出版商:Taylor & Francis Group    

年代:1961

数据来源: Taylor

ISSN:0162-1459    

DOI:10.1080/01621459.1961.10480658

出版商:Taylor & Francis Group    

年代:1961

数据来源: Taylor

摘要:

Sample Design in Business Research.W. Edwards Deming. New York: John Wiley and Sons, 1960. Pp. xix, 631. $12.00. Reviewed by Leslie Kish

ISSN:0162-1459    

DOI:10.1080/01621459.1961.10480659

出版商:Taylor & Francis Group    

年代:1961

数据来源: Taylor