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891.
892.
Let X1, X2, …, Xm be successive observations on m objects, numbered 1,2, …, m. If X1 belongs to the n largest observations among X1,X2,…,Xi, object i is called a record, i = 1,2,…,m; n?1.In investigating the influence of the ranking of the objects on the expected number of records, a hierarchy of stochastic order relations between random variables arises.It is these order relations and their relationship with known stochastic orderings that are studied in this paper. 相似文献
893.
Friedrich Pukelsheim 《Journal of statistical planning and inference》1980,4(4):339-364
Necessary and sufficient conditions are established when a continuous design contains maximal information for a prescribed s-dimensional parameter in a classical linear model. The development is based on a thorough study of a particular dual problem and its interplay with the optimal design problem, extending partial results and earlier approaches based on differential calculus, game theory, and other programming methods. The results apply in particular to a class of information functionals which covers c-, D-, A-, L-optimality, they include a complete account of the non-differentiable criterion of E-optimality, and provide a constructive treatment of those situations in which the information matrix is singular. Corollaries pertain to the case of s out of k parameters, simultaneous optimality with respect to several criteria, multiplicity of optimal designs, bounds on their weights, and optimality which is induced by admissibility. 相似文献
894.
In sampling from a continuous distribution with unknown mean μ and variance σ2 the problem of estimation of μ, when it is known that μ∈(a, ∞) (or μ∈(-∞, b)), is considered. The estimators proposed here lie in the interval (a, ∞) (or (-∞, b)) almost surely. The performance of these estimators is compared to that of some known estimators in the case of sampling from a normal, exponential and a weighted difference of two independent chi-square distributions. 相似文献
895.
The problem of embedding an orthogonal array of strength 2 into a complete orthogonal array is discussed. It is shown that for any n≠4 any orthogonal array of strength 2 and deficiency 2 can always be embedded into a corresponding complete orthogonal array. 相似文献
896.
This paper describes the basic structure of the Global Model used in preparing various parts of the World Development Report (WDR) issued annually by the World Bank. The report is designed to help clarify linkages between the international economy and the domestic strategies of developing countries. The paper is divided in four parts. The first two present different aspects of the model structure and discuss the reasons that induced the authors to orient themselves towards given functional specifications. In the final parts the policy relevance of the exercise is studied in light of the results that the model has produced for 1975–1985. 相似文献
897.
In the usual two-way layout of ANOVA (interactions are admitted) let nij ? 1 be the number of observations for the factor-level combination(i, j). For testing the hypothesis that all main effects of the first factor vanish numbers are given such that the power function of the F-test is uniformly maximized (U-optimality), if one considers only designs (nij) for which the row-sums ni are prescribed. Furthermore, in the (larger) set of all designs for which the total number of observations is given, all D-optimum designs are constructed. 相似文献
898.
Power studies of tests of equality of covariance matrices of two p-variate complex normal populations σ1 = σ2 against two-sided alternatives have been made based on the following five criteria: (1) Roy's largest root, (2) Hotelling's trace, (4) Wilks' criterion and (5) Roy's largest and smallest roots. Some theorems on transformations and Jacobians in the two-sample complex Gaussian case have been proved in order to obtain a general theorem for establishing the local unbiasedness conditions connecting the two critical values for tests (1)–(5). Extensive unbiased power tabulations have been made for p=2, for various values of n1, n2, λ1 and λ2 where n1 is the df of the SP matrix from the ith sample and λ1 is the ith latent root of σ1σ-12 (i=1, 2). Equal tail areas approach has also been used further to compute powers of tests (1)–(4) for p=2 for studying the bias and facilitating comparisons with powers in the unbiased case. The inferences have been found similar to those in the real case. (Chu and Pillai, Ann. Inst. Statist. Math. 31. 相似文献
899.
Designs for quadratic and cubic regression are considered when the possible choices of the controlable variable are points x=( x1,x2,…,xq) in the q-dimensional. Full of radius R, Bq(R) ={x:Σ4ix2i?R2}. The designs that are optimum among rotatable designs with respect to the D-, A-, and E-optimality criteria are compared in their performance relative to these and other criteria, including extrapolation. Additionally, the performance of a design optimum for one value of R, when it is implemented for a different value of R, is investigated. Some of the results are developed algebraically; others, numerically. For example, in quadratic regression the A-optimum design appears to be fairly robust in its efficiency, under variation of criterion. 相似文献
900.
Anil K. Bhargava 《Journal of statistical planning and inference》1979,3(1):19-26
A multivariate “errors in variables” regression model is proposed which generalizes a model previously considered by Gleser and Watson (1973). Maximum likelihood estimators [MLE's] for the parameters of this model are obtained, and the consistency properties of these estimators are investigated. Distribution of the MLE of the “error” variance is obtained in a simple case while the mean and the variance of the estimator are obtained in this case without appealing to the exact distribution. 相似文献