摘要:

Abstract and SummaryThe existence of a component of variance for competition among sampling units or among individuals in a group was discussed by Yates and Zacopany in 1935. No procedure was suggested for estimating this component of variance. It is the purpose of this paper to give a procedure for estimating the component of variance due to competition and to apply the procedure to a set of data on weaning weights of pigs with 116 litters of various sizes and for Yorkshire, Chester‐White, and Berkshire breeds. The first problem was to define litter size. Within this definition then, litters sizes of 3 to 14 pigs per litter were obtained. The variation among pigs within a litter of size h was considered to have an expected value equal to Vs+ Vchwhere Vsis the sampling variance component and Vchis the competition variance component for a litter of size h. In order to obtain an estimate of Vch, a polynomial relation between h and Vchwas postulated. In particular, it was postulated thatwhere E(.) denotes expected value. This form states that Vchgoes to zero for one pig per litter; it may be appropriate as long as small litter sizes (say 1 and 2 at least) are omitted from the analysis as was done in the present instance.Using an iterative procedure of reestimating the weights at each stage, a form of weighted least squares analysis was performed. The procedure appears to converge after three to four steps of iteration. Solutions for some or all of the parameters Vp, Vs, β1and β2for h even, h odd, and all h = 3, 4, …, 14, were obtained using among litter mean squares, Ah, only, using within litter mean squares, Wh, only, and using both Ah, and Whvalues. The Ahvalues for h = 3, 4, and 5 appeared to form a different group than for the other values of h. Both the Ahand Whmean squares were from 56 day weights adjusted for birth weight.The maximum value of Vchfor odd h, was nine whereas it was six for even h. Using all h the maximum value for Vchoccurred when h was equal to nine. It appeared that expressing Vchas a quadratic function of litter size was satisfactory for these litter sizes and mean sq

ISSN:0004-9581    

DOI:10.1111/j.1467-842X.1978.tb01296.x

出版商:Blackwell Publishing Ltd    

年代:1978

数据来源: WILEY

摘要:

AbstractSome programmes of experimentation require the superimposition of a new set of treatments on an existing experiment. Randomization of such treatments has received little attention in the literature but merits careful consideration. The present paper examines two apparently different theoretical approaches, one in effect randomizing the experiments together and the other randomizing the second experiment without reference to any randomization used in the first. In the simplest superimpositions the two methods give identical results in practice but problems arise when one Latin square is to be superimposed on another.

ISSN:0004-9581    

DOI:10.1111/j.1467-842X.1978.tb01297.x

出版商:Blackwell Publishing Ltd    

年代:1978

数据来源: WILEY

ISSN:0004-9581    

DOI:10.1111/j.1467-842X.1978.tb01298.x

出版商:Blackwell Publishing Ltd    

年代:1978

数据来源: WILEY

ISSN:0004-9581    

DOI:10.1111/j.1467-842X.1978.tb01299.x

出版商:Blackwell Publishing Ltd    

年代:1978

数据来源: WILEY

ISSN:0004-9581    

DOI:10.1111/j.1467-842X.1978.tb01300.x

出版商:Blackwell Publishing Ltd    

年代:1978

数据来源: WILEY

ISSN:0004-9581    

DOI:10.1111/j.1467-842X.1978.tb01301.x

出版商:Blackwell Publishing Ltd    

年代:1978

数据来源: WILEY

摘要:

SummaryNumerical results are presented for estimates of the parameters in the linear model Y =βX +ε in which X is normally distributed and ε is symmetric stable. The study complements an earlier paper of the same title and the main concern is with numerical comparisons between four estimates of β; the least squares estimate, the minimum absolute deviations estimate, and two moment estimates of the form derived in Chambers and Heathcote (1975). The generation of fifty independent sets of observations (Xj, Yj), j = 1,2, …, n for each of n = 100, 500 and selected combinations of parameter values provided the basis of the results. It is indicated that the moment estimators and the minimum absolute deviation estimator performed comparably, and are a significant improvement on the least squares estimator. The main conclusion is that one of the moment estimates, based on a two stage adaptive procedure and denoted by β¯n(ta) below, is generally the most useful of t

ISSN:0004-9581    

DOI:10.1111/j.1467-842X.1978.tb01302.x

出版商:Blackwell Publishing Ltd    

年代:1978

数据来源: WILEY

ISSN:0004-9581    

DOI:10.1111/j.1467-842X.1978.tb01303.x

出版商:Blackwell Publishing Ltd    

年代:1978

数据来源: WILEY

ISSN:0004-9581    

DOI:10.1111/j.1467-842X.1978.tb01304.x

出版商:Blackwell Publishing Ltd    

年代:1978

数据来源: WILEY

摘要:

Book reviewed in this article:Shenton, L. R. and Bowman, K. O. Maximum Likelihood Estimation in Small Samples.Bierman, G. J. Factorization Methods for Discrete Sequential EstimationKendall, Sir Maurice and Plackett, R. L. (Eds). Studies in the History of Statistics and Probability.

ISSN:0004-9581    

DOI:10.1111/j.1467-842X.1978.tb01305.x

出版商:Blackwell Publishing Ltd    

年代:1978

数据来源: WILEY