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1.
Friedrich Pukelsheim 《统计学通讯:理论与方法》2013,42(7):603-610
Equality is shown of the g-inverse and Moore-Penrose inverse representation of the BLUE in the general linear model. The proof is based on a matrix identity which allows also to establish a functional relationship between the BLUE and Ridge-type estimates. 相似文献
2.
C. A. McGilchrist R. L. Sandland J. L. Hennessy 《Australian & New Zealand Journal of Statistics》1983,25(2):321-328
Recursive methods in regression have proved useful in providing diagnostic tools for checking the model as well as checking the stability of the model over time. Such methods are now extended to deal with the problems of singularity that arise when one variable is completely confounded with previously fitted variables up to a particular time point. The problem is solved by setting it in the framework of the general linear model with dependent errors. 相似文献
3.
A general computer program which generates either the Wilcoxon, Kruskal-Wallis, Friedman, or extended Friedman statistic (where the numbers of cell observations nij may be any positive integer or zero) can be formulated simply by using the computational algorithm for the Benard-Van Elteren statistic. It is shown that the Benard-Van Elteren statistic can be computed using matrix algebra subroutines including multiplication and inverse or g-inverse computational algorithms in the case where the rank of the matrix V of the variances and covariances of the column totals is k-1. For the case where the rank of V is less than k-1 the use of the g-inverse is shown to greatly reduce the labors of calculation. In addition, the use of the Benard-Van Elteren statistic in testing against ordered alternatives is indicated. 相似文献
4.
A general definition of a set of projectors for decomposing a vector as the sum of vectors belonging to disjoint subspaces not necessarily spanning the whole space is given. Such projectors are defined only over the union of the disjoint subspaces. But their extension to the whole space is of some interest in statistical problems. Explicit expressions are obtained for projectors and their extensions in terms of matrices spanning the subspaces and g-inverses. Decomposition of a projector as the sum of projectors on subspaces is obtained and applied to problems arising in correlation analysis, analysis of variance and estimation of parameters in the Gauss-Markoff model. 相似文献
5.
Avinash C Singh 《统计学通讯:理论与方法》2013,42(11):3255-3273
6.
G. SadasIvan 《统计学通讯:理论与方法》2013,42(7):821-833
In paired comparison experiments t objects are ranked for any particular characteristic x by offering the objects in all possible pairs to a judge, each pair being repeated a certain number of times. The judge is to express his preference by giving a score 1 to the preferred object and a score 0 to the non-preferred object. A modification of Thurstone Model for analysis of data from such experiments has been given by Mosteller ‘1951a,b,c’. In this paper angular transformation is used to generalize Mosteller1s model in order to make the preference proportions independent and incidentally ensure homo-scedastlcity of variances and correlations and additivlty of scale in the subjective continuum for the stimuli." The model is extended to unequal numbers of repetitions of the pairs. Using the model two different types of treatment ratings are obtained along with the respective standard errors for moderately large numbers of repetitions, one setting the location parameter S, "0 and the other using the constraint S1 + S2 +…,+ St = 0. 相似文献
7.
Wiktor Oktaba 《Australian & New Zealand Journal of Statistics》2003,45(2):195-205
The aim of the paper is to generalize testing and estimation for the multivariate standard incomplete block model (Rao & Mitra, 1971a) to the general multivariate Gauss—Markov incomplete block model with singular covariance matrix. The results of this paper can be applied to particular cases of the multivariate Gauss—Markov incomplete block model, including the Zyskind—Martin model. 相似文献
8.
C. Radhakrishna Rao 《统计学通讯:理论与方法》2013,42(13):1119-1208
In this paper we obtain the complete class of representations and useful subclasses of MV-UB-LE and MV-MB-LE (minimum variance unbiased and minimum bias linear estimators) of linear parametric functions in the Gauss-Markoff model (Y,Xβ, σ 2V) when V is possibly singular. 相似文献
9.
Summary Two quadratic formsS
H andS
E for a testable hypothesis and for an error in the multivariate Zyskind-Martin model with singular covariance matrix are expressed
by means of projector operators. Thus the results for the multivariate standard model with identity covariance matrix given
by Humak (1977) and Christensen (1987, 1991) are generalized for the case of Zyskind-Martin model. Special cases of our results
are formulae forS
H andS
E in Aitken's (1935) model. In the case of general Gauss-Markoff modelS
H andS
E can also be expressed by means of projector operators for some subclasses of testable hypotheses. For these hypotheses, testing
in Gauss-Markoff model is equivalent to testing in a Zyskind-Martin model. 相似文献
10.
S. Gabler 《Statistical Papers》1990,31(1):225-231
In sampling from finite populations conditional minimax estimators are equivalent to BLU estimators. This has been shown by
Gabler (1988). If the covariance matrix is singular the BLU estimator can be represented in two different ways. 相似文献