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41.
42.
An asymptotic series for sums of powers of binomial coefficients is derived, the general term being defined and usable with a computer symbolic language. Sums of squares of coefficients in the symmetric case are shown to have a link with classical moment problems, but this property breaks down for cubes and higher powers. Problems of remainders for the asymptotic series are mentioned. Using the reflection formula for I'(.), a continuous form for a binomial function is set up, and this becomes oscillatory outstde the usual range. A new contmued fraction emerges for the logarithm of an adjusted sum of binomial squares. The note is a contribution to the problem of the interpretation of asymptotic series and processes for their convergence acceleration. 相似文献
43.
A multiparameter extension is made to modified two stage shrinkage estimator proposed by Handa andKambo (1990), For aparticular class of shrinkage estimator, the local optimality of the extended modified estimator is shown over the two stage shrinkage estimator defined by Bhattacharya and Prakasa Rao(1990) in terms of quadratic loss. 相似文献
44.
In a series of papers, Kshirsagar (1964, 1971) and McHenry and Kshirsagar (1977), factorize Wilks' A into a number of factors and find the independent null multivariate beta densities of these factors. These factors are the likelihood ratio test criteria for testing the goodness of fit of certain assigned discriminant functions or canonical variables either in the space of independent or dependent variables. Essentially the factors of Wilks' A are the factors of certain multivariate beta distributed matrix or its determinant. The Bartlett decomposition of the underlying multivariate beta distribution into independent factors determines the distribution of these factors. The present paper generalizes Kshirsagar's (1971) normal theory to the elliptically contoured model, and shows that his results are null robust for the elliptically contoured model. 相似文献
45.
Lot resubmissions are allowed in situations where the original inspection results are suspected or when the supplier is allowed to opt for resampling as per the provisions of the contract etc. This paper examines the situation of resampling of lots and derives the performance measures of a resampling scheme having a single sampling plan for inspection. The usefulness and limitations of resampling of resubmitted lots are also discussed 相似文献
46.
This article describes estimation and inference procedures for the parameters of the Box-Cox and foided-power transformations in repeated measures and growth curve models. Procedures for computing maximum likelihood estimates of the transformation and covariance parameters under several covanance structures (omnibus sphericity, local sphericity, and unstructured) are described. Lack of fit statistics and hypothesis tests for comparing these structures also are described. The procedures are illustrated on three data sets. Software for performing the analyses in the SAS System is described and is available from the authors. 相似文献
47.
A. K. Md. Ehsanes Saleh 《统计学通讯:理论与方法》2013,42(11):3145-3157
ABSTRACTThis article considers the estimation of a distribution function FX(x) based on a random sample X1, X2, …, Xn when the sample is suspected to come from a close-by distribution F0(x). The new estimators, namely the preliminary test (PTE) and Stein-type estimator (SE) are defined and compared with the “empirical distribution function” (edf) under local departure. In this case, we show that Stein-type estimators are superior to edf and PTE is superior to edf when it is close to F0(x). As a by-product similar estimators are proposed for population quantiles. 相似文献
48.
ABSTRACTIn this paper, we extend a variance shift model, previously considered in the linear mixed models, to the linear mixed measurement error models using the corrected likelihood of Nakamura (1990). This model assumes that a single outlier arises from an observation with inflated variance. We derive the score test and the analogue of the likelihood ratio test, to assess whether the ith observation has inflated variance. A parametric bootstrap procedure is implemented to obtain empirical distributions of the test statistics. Finally, results of a simulation study and an example of real data are presented to illustrate the performance of proposed tests. 相似文献
49.
This paper deals with the problem of selecting the “best” population from a given number of populations in a decision theoretic framework. The class of selection rules considered is based on a suitable partition of the sample space. A selection rule is given which is shown to have certain optimum properties among the selection rules in the given class for a mal rules are known. 相似文献
50.
The authors establish the joint distribution of the sum X and the maximum Y of IID exponential random variables. They derive exact formuli describing the random vector (X, Y), including its joint PDF, CDF, and other characteristics; marginal and conditional distributions; moments and related parameters; and stochastic representations leading to further properties of infinite divisibility and self-decomposability. The authors also discuss parameter estimation and include an example from climatology that illustrates the modeling potential of this new bivariate model. 相似文献