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101.
102.
Consider a skewed population. Suppose an intelligent guess could be made about an interval that contains the population mean. There may exist biased estimators with smaller mean squared error than the arithmetic mean within such an interval. This article indicates when it is advisable to shrink the arithmetic mean towards a guessed interval using root estimators. The goal is to obtain an estimator that is better near the average of natural origins. An estimator proposed. This estimator contains the Thompson (1968) ordinary shrinkage estimator, the Jenkins et al. (1973) square-root estimator, and the arithmetic sample mean as special cases. The bias and the mean squared error of the proposed more general estimator is compared with the three special cases. Shrinkage coefficients that yield minimum mean squared error estimators are obtained. The proposed estimator is considerably more efficient than the three special cases. This remains true for highly skewed populations. The merits of the proposed shrinkage square-root estimator are supported by the results of numerical and simulation studies. 相似文献
103.
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
104.
There is a considerable amount of literature dealing with inference about the parameters in a heteroscedastic one-way random-effects ANOVA model. In this paper, we primarily address the problem of improved quadratic estimation of the random-effect variance component. It turns out that such estimators with a smaller mean squared error compared with some standard unbiased quadratic estimators exist under quite general conditions. Improved estimators of the error variance components are also established. 相似文献
105.
In this paper, we extend the work of Gjestvang and Singh [A new randomized response model, J. R. Statist. Soc. Ser. B (Methodological) 68 (2006), pp. 523–530] to propose a new unrelated question randomized response model that can be used for any sampling scheme. The interesting thing is that the estimator based on one sample is free from the use of known proportion of an unrelated character, unlike Horvitz et al. [The unrelated question randomized response model, Social Statistics Section, Proceedings of the American Statistical Association, 1967, pp. 65–72], Greenberg et al. [The unrelated question randomized response model: Theoretical framework, J. Amer. Statist. Assoc. 64 (1969), pp. 520–539] and Mangat et al. [An improved unrelated question randomized response strategy, Calcutta Statist. Assoc. Bull. 42 (1992), pp. 167–168] models. The relative efficiency of the proposed model with respect to the existing competitors has been studied. 相似文献
106.
In this paper, we develop a generalized version of the two-piece skew normal distribution of Kim [On a class of two-piece skew-normal distributions, Statistics 39(6) (2005), pp. 537–553] and derive explicit expressions for its distribution function and characteristic function and discuss some of its important properties. Further estimation of the parameters of the generalized distribution is carried out. 相似文献
107.
Orthogonal block designs in mixture experiments have been extensively studied by various authors. Aggarwal et al. [M.L. Aggarwal, P. Singh, V. Sarin, and B. Husain, Mixture designs in orthogonal blocks using F-squares, METRON – Int. J. Statist. LXVII(2) (2009), pp. 105–128] considered the case of components assuming the same volume fractions and obtained mixture designs in orthogonal blocks using F-squares. In this paper, we have used the class of designs presented by Aggarwal et al. and have obtained D-, A- and E-optimal orthogonal block designs for four components in two blocks for Becker's mixture models and K-model, respectively. Orthogonality conditions for the considered models are also given. 相似文献
108.
Arabin Kumar Dey 《Statistics》2013,47(2):197-214
Log-normal and Weibull distributions are the two most popular distributions for analysing lifetime data. In this paper, we consider the problem of discriminating between the two distribution functions. It is assumed that the data are coming either from log-normal or Weibull distributions and that they are Type-II censored. We use the difference of the maximized log-likelihood functions, in discriminating between the two distribution functions. We obtain the asymptotic distribution of the discrimination statistic. It is used to determine the probability of correct selection in this discrimination process. We perform some simulation studies to observe how the asymptotic results work for different sample sizes and for different censoring proportions. It is observed that the asymptotic results work quite well even for small sizes if the censoring proportions are not very low. We further suggest a modified discrimination procedure. Two real data sets are analysed for illustrative purposes. 相似文献
109.
For the two-sample location problem with continuous data we consider a general class of tests, all members of it are based on U-statistics. The asymptotic efficacies are investigated in detail. We construct an adaptive test where all statistics involved are suitably chosen U-statistics. It is shown that the proposed adaptive test has good asymptotic and finite sample power properties. 相似文献
110.