摘要:

GivenNpoints independently drawn from the uniform distribution on (0, 1), let ᵱnbe the size of the smallest interval that containsnout of theNpoints; let ñpbe the largest number of points to be found in any subinterval of (0, 1) of lengthp.This paper uses a result of Karlin, McGregor, Barton, and Mallows to determine the distribution of ñp, forp= 1/k, kan integer. The paper gives simple determinations for the expectations and variances of ᵱn, for all fixedn> (N+ 1)/2, and of ñ1/2. The distribution and expectation of ñpare estimated and tabulated for the casesp= 0.1(0.1)0.9,N= 2(1)10.

ISSN:0162-1459    

DOI:10.1080/01621459.1966.10482203

出版商:Taylor & Francis Group    

年代:1966

数据来源: Taylor

ISSN:0162-1459    

DOI:10.1080/01621459.1966.10482204

出版商:Taylor & Francis Group    

年代:1966

数据来源: Taylor

摘要:

In a recent paper in this Journal, Rothenberg, Fisher and Tilanus [1] discuss a class of estimators of the location parameter of the Cauchy distribution, taking the form of the arithmetic average of a central subset of the sample order statistics. They show that the average of roughly the middle quarter of the ordered sample has minimum asymptotic variance within this class, and that asymptotically it eliminates about 36 per cent of the efficiency loss of the median (the most commonly used estimator) in comparison to the maximum likelihood estimator (m.l.e.). Of course both the m.l.e. and the best linear unbiased estimator based on the order statistics (BLUE) achieve full asymptotic efficiency in the Cramér-Rao sense and there can be no dispute about the relative merits of the three estimators asymptotically, or about the inferiority of the median (with asymptotic efficiency 8/π2ė 0.8 compared with about 0.88 for the estimator of Rothenberg et al.).

ISSN:0162-1459    

DOI:10.1080/01621459.1966.10482205

出版商:Taylor & Francis Group    

年代:1966

数据来源: Taylor

摘要:

As is well known, the U. S. national accounts contain a “Statistical Discrepancy” which serves to reconcile estimates ofGNPfrom the product and from the income side. While the Discrepancy is a measure only of overall consistency rather than of error, its magnitude and pattern over time do give some indication of the quality of the national accounts data. In the past, the Statistical Discrepancy has not always behaved as a quantitatively unimportant random error term—a disturbing sign with regard to theGNPstatistics. The presence of a systematic Discrepancy also causes difficulties in some specific problems. For example, it is necessary to assume a value for the Discrepancy in the identities of an econometric model when forecasts are made. The Discrepancy can also seriously affect estimates involving thoseGNPcategories, such as savings, which are customarily calculated as residuals with the consequence that the Discrepancy is allocated to them.

ISSN:0162-1459    

DOI:10.1080/01621459.1966.10482206

出版商:Taylor & Francis Group    

年代:1966

数据来源: Taylor

摘要:

Statistical Theory and Methodology in Science and Engineering, Second Edition.K. A. Brownlee.John Wiley and Sons, Inc., 1965. Pp. xvi, 590. $18.50. Reviewed by R. J. Hader

ISSN:0162-1459    

DOI:10.1080/01621459.1966.10482207

出版商:Taylor & Francis Group    

年代:1966

数据来源: Taylor

ISSN:0162-1459    

DOI:10.1080/01621459.1966.10482208

出版商:Taylor & Francis Group    

年代:1966

数据来源: Taylor

摘要:

This article has no abstract

ISSN:0162-1459    

DOI:10.1080/01621459.1966.10482182

出版商:Taylor & Francis Group    

年代:1966

数据来源: Taylor