摘要:

Bose and Shimamoto [1] have shown that partially Balanced Incomplete Block (PBIB) designs are characterized by association schemes. But in the PBIB designs discussed so far by the various authors the relation of association is symmetrical or reflexive. The object of this paper is to study a class of useful designs in which the relation of association is not necessarily symmetrical. First the definition of this new design is given. The relation between the parameters and the number of independent secondary parameters are discussed next. Two types of association schemes are given defined as type I and type II, the latter being based on Galois Fields. For the general method of analysis, the model assumed is that of a design for two-way elimination of heterogeneity. The final equations arrived at are the same as those for PBIB designs. A numerical example illustrates the method still further. Two methods of construction, one each for type I and type II are given. The method for type II is based on the property of Galois Fields.

ISSN:0162-1459    

DOI:10.1080/01621459.1964.10480729

出版商:Taylor & Francis Group    

年代:1964

数据来源: Taylor

摘要:

An intuitive estimate is presented for estimating linear regression coefficients when an unspecified number and pattern of the independent variables for some individuals are not observed. It is shown that the efficiency of this approach depends upon the correlation among the independent variables as well as the proportion of observations which is missing.

ISSN:0162-1459    

DOI:10.1080/01621459.1964.10480730

出版商:Taylor & Francis Group    

年代:1964

数据来源: Taylor

摘要:

This article develops a method of calculating iterative estimates of the coefficients of a set of linear regression equations. There arepequations such that the explanatory variables are non-stochastic and it is assumed that the random disturbances of at least one pair of equations are correlated. Provided that either different explanatory variables enter the various equations or that if the same explanatory variables enter then the observations are different, it is possible to obtain estimators that are asymptotically more efficient than the simple one-at-a-time least squares estimators. The estimators developed herein are calculated recursively using the Gauss-Seidel method of iteration. It is shown that all of the iterations are asymptotically normal, and that in the limit the iterations have the same asymptotic distribution as the generalized least squares estimator proposed by Zellner. The iterative estimators directly exploit the correlations among the random disturbances. In additionplinear regression equations are defined such that in theith equation the dependent variable is the residual of the originalith equation and thep− 1 “explanatory” variables are the residuals of all other regressions. It is shown that the regression coefficients of these residuals can be estimated recursively, jointly with the original regression coefficients, or directly from the one-at-a-time least squares residuals. All of these estimators of the regression coefficients of the random disturbances converge in distribution to the same multivariate normal law.

ISSN:0162-1459    

DOI:10.1080/01621459.1964.10480731

出版商:Taylor & Francis Group    

年代:1964

数据来源: Taylor

摘要:

When measurements are made on the same experimental item at successive stages of an experiment, the experimental errors include components which are cumulative in nature, and are hence not independent. This dependence may be removed by using incremental changes in the experimental item as the yield variable, and then using a weighted least squares approach to estimate the parameters of the model, assumed to be linear. Alternately, the original cumulative data may be used directly, and Aitken's method of weighted least squares applied to obtain the parameter estimates. These estimates are shown to be identical.

ISSN:0162-1459    

DOI:10.1080/01621459.1964.10480732

出版商:Taylor & Francis Group    

年代:1964

数据来源: Taylor

摘要:

The bounds for the number of common treatments between any two blocks of a semi-regular group divisible design are derived using the characteristic roots ofNN′ whereNis the incidence matrix of the design. It is further shown that these bounds are superior to the existing ones. Some new results are obtained and known ones are established in an elegant way.

ISSN:0162-1459    

DOI:10.1080/01621459.1964.10480733

出版商:Taylor & Francis Group    

年代:1964

数据来源: Taylor

ISSN:0162-1459    

DOI:10.1080/01621459.1964.10480734

出版商:Taylor & Francis Group    

年代:1964

数据来源: Taylor

摘要:

Distributions are derived of the product and of the quotient of maximum values in samples from a population described by the frequency αxk, which may be called a power-function population. The distribution of the quotient is used to test whether two samples have come from the same triangular population. Estimators of the parameters of the distribution are derived.

ISSN:0162-1459    

DOI:10.1080/01621459.1964.10480735

出版商:Taylor & Francis Group    

年代:1964

数据来源: Taylor

摘要:

Basmann [4] has recently obtained some results of the exact sampling distributions of the generalized classical linear (GCL) estimators of the parameters of a system of three simultaneous structural linear equations These results appear as generalizations of earlier results given by Basmann [5] for a system of two equations. Kabe [9] used the known properties of the noncentral Wishart distribution to give an alternative derivation of Basmann's results for the two-equation case. In view of the importance of the GCL estimators in econometric statistics, it seems useful to derive Basmann's three-equation case results [4], by using some properties of the non-central Wishart distribution. Some applications of the noncentral Wishart distribution theory to the problem of estimating stochastic structural linear relations have been pointed out earlier by Anderson [1, p. 410, second paragraph]. The results derived here appear as generalizations of the results in reference [9] and include some extensions of Basmann's results.

ISSN:0162-1459    

DOI:10.1080/01621459.1964.10480736

出版商:Taylor & Francis Group    

年代:1964

数据来源: Taylor

摘要:

An examination is made of the accuracy of the usual approximation used for the variance of the ratio estimate. It is shown that, under certain conditions, the usual approximation understates the true variance by an amount depending upon the distribution of the sample mean of the auxiliary variate.

ISSN:0162-1459    

DOI:10.1080/01621459.1964.10480737

出版商:Taylor & Francis Group    

年代:1964

数据来源: Taylor

摘要:

An approximation of the exact distribution of the Wilcoxon test for symmetry by means of an Edgeworth series is derived. Probabilities are computed for sample sizesN= 10(1)26(2)42(3)48,50,100, and the accuracy investigated and compared with that of the normal approximation. The Edgeworth expansion gives a very satisfactory approximation forN≥ 15 (maximum error < 25×10−5when taken to terms of order 1/Nand < 6×10−5to terms of order 1/N2, for a standardized variable (x) in the region 1.75 ≤x≤ 3.1). ForN= 20 the Edgeworth approximation almost coincides with the exact distribution. ForN >20 where no exact probabilities are readily available, the accuracy of the normal distribution is investigated relative to the Edgeworth expansion to terms of order 1/N2. The validity of this procedure is established by calculating certain exact probabilities in the interval studied, for values ofN= 21, 22 and 25.

ISSN:0162-1459    

DOI:10.1080/01621459.1964.10480738

出版商:Taylor & Francis Group    

年代:1964

数据来源: Taylor