共查询到20条相似文献,搜索用时 31 毫秒
1.
Minimax estimators for the lower-bounded scale parameter of a location-scale family of distributions
This article is concerned with the minimax estimation of a scale parameter under the quadratic loss function where the family of densities is location-scale type. We obtain results for the case when the scale parameter is bounded below by a known constant. Implications for the estimation of a lower-bounded scale parameter of an exponential distribution are presented under unknown location. Furthermore, classes of improved minimax estimators are derived for the restricted parameter using the Integral Expression for Risk Difference (IERD) approach of Kubokawa (1994). These classes are shown to include some existing estimators from literature. 相似文献
2.
Yougui Wu 《统计学通讯:理论与方法》2020,49(6):1446-1461
AbstractIn diagnostic trials, clustered data are obtained when several subunits of the same patient are observed. Intracluster correlations need to be taken into account when analyzing such clustered data. A nonparametric method has been proposed by Obuchowski (1997) to estimate the Receiver Operating Characteristic curve area (AUC) for such clustered data. However, Obuchowski’s estimator is not efficient as it gives equal weight to all pairwise rankings within and between cluster. In this paper, we propose a more efficient nonparametric AUC estimator with two sets of optimal weights. Simulation results show that the loss of efficiency of Obuchowski’s estimator for a single AUC or the AUC difference can be substantial when there is a moderate intracluster test correlation and the cluster size is large. The efficiency gain of our weighted AUC estimator for a single AUC or the AUC difference is further illustrated using the data from a study of screening tests for neonatal hearing. 相似文献
3.
AbstractIn this article, we propose new efficient and more generalized difference-cum-exponential type estimator and generalized-difference-cum-generalized exponential type estimators for estimating the mean of sensitivity variable using the auxiliary information. We also discuss theoretically that proposed generalized estimators are more efficient than Sousa et al. (2010), Gupta et al. (2012) and Koyuncu, Gupta, and Sousa (2014) estimators. Results from a real life application and simulation study are presented to demonstrate the performance of the proposed mean estimators in relation to some of the existing mean estimators. 相似文献
4.
AbstractComplete expectation of life of an individual gives an intuitive and interesting perspective on the ageing process and is an important concept in the insurance sector for determination of premium. We propose a new test for testing equality of complete expectations of life of two groups/populations. Power of the new test is calculated through simulations and compared with the power of the tests given by Berger, Boos, and Guess (1988) and Aly (1997). It is observed that the proposed test statistic is more powerful than the competing tests for the cases considered in this paper. A real life illustration is included. 相似文献
5.
Guangyu Mao 《统计学通讯:理论与方法》2020,49(14):3572-3584
AbstractThis paper investigates a class of statistics based on Pearson’s correlation coefficient for testing the mutual independence of a random vector in high dimensions. Two existing statistics, proposed by Schott (2005) and Mao (2014) respectively, are special cases of the class. A generic testing theory for the class of statistics is developed, which clarifies under what conditions the class of statistics can be employed for the testing purpose. By virtue of the theory, three new tests are introduced, and related statistical properties are discussed. To examine our theoretical findings and check the performance of the new tests, simulation studies are applied. The simulation results justify the theoretical findings and show that the newly introduced tests perform well, as long as both the dimension and the sample size of the data are moderately large. 相似文献
6.
Jie Li 《统计学通讯:理论与方法》2020,49(22):5613-5626
AbstractIn this paper, we establish the complete convergence and complete integral convergence for arrays of row-wise extended independent random variables under sub-linear expectation space with some conditions. At the same time we extend some complete convergence and complete integral convergence theorems from the classical probability space to the sub-linear expectation space. The results generalize corresponding results obtained by Wu et al. (2017). 相似文献
7.
Hu Yang 《统计学通讯:理论与方法》2013,42(1):70-80
Sakall?oglu et al. (2001) dealt with the comparisons among the ridge estimator, Liu estimator, and iteration estimator. Akdeniz and Erol (2003) have compared the (almost unbiased) generalized ridge regression estimator with the (almost unbiased) generalized Liu estimator in the matrix mean squared error sense. In this article, we study the ridge estimator and Liu estimator with respect to linear equality restriction, and establish some sufficient conditions for the superiority of the restricted ridge estimator over the restricted Liu estimator and the superiority of the restricted Liu estimator over the restricted ridge estimator under mean squared error matrix, respectively. Furthermore, we give a numerical example. 相似文献
8.
《统计学通讯:理论与方法》2012,41(2):343-360
AbstractThis paper presents the robust Bayesian inference based on the γ-divergence which is the same divergence as “type 0 divergence” in Jones et al. (2001) on the basis of Windham (1995). It is known that the minimum γ-divergence estimator works well to estimate the probability density for heavily contaminated data, and to estimate the variance parameters. In this paper, we propose a robust posterior distribution against outliers based on the γ-divergence and show the asymptotic properties of the proposed estimator. We also discuss some robustness properties of the proposed estimator and illustrate its performances in some simulation studies. 相似文献
9.
Julián de la Horra 《统计学通讯:理论与方法》2013,42(10):1905-1914
The positive false discovery rate was introduced by Storey (2003) as an alternative to the family wise error rate for the case in which we are simultaneously testing a large amount of hypotheses. The positive false discovery rate has a very nice Bayesian interpretation (as it was shown by Storey, 2003) and its robustness is analyzed. The emphasis is on the ε-contamination class (one of the most used classes of priors for Bayesian robustness) and it is shown that robustness is not obtained when the basic prior concentrates the probability on the null hypothesis. 相似文献
10.
In this article, we introduce a new method for the volatility function estimation of continuous-time diffusion process dX t = μ(X t )dt + σ(X t )dW t , which is based on combining the idea of local linear smoother and variable bandwidth. We give the expressions for the conditional MSE and MISE of the estimator and obtain the optimal variable bandwidth. An explicit formula for the optimal variable bandwidth is presented by minimizing the MISE, which extends the related results in Fan and Gijbels (1992), etc. Finally, some simulations show that the performance of the proposed estimator with optimal variable bandwidth is often much better than that of the local linear estimator with invariable bandwidth. 相似文献
11.
AbstractWeak convergence and moment convergence issues are investigated for the New Better than Average Failure Rate (NBAFR) family (introduced by Loh (1984)). We explore the validity of these results in the context of a more general ageing class that we introduce. We prove some new properties of this class and derive its interrelationships with other non-monotonic ageing families. Reliability and moment bounds are obtained and an interesting characterization of exponentiality is proved. Special cases of our results lead to new theorems for the NBAFR class. Finally weak convergence and related issues are established for this class. 相似文献
12.
AbstractIn this paper, compared with the results in Janson (2018), we provide some improved explicit bounds for the tail probabilities of the sum of independent geometric variables with their expectations and variances. Particularly, in some cases, we demonstrate that our bounds are sharper than the ones in Janson (2018). 相似文献
13.
《统计学通讯:理论与方法》2013,42(6):1119-1133
Abstract For randomly censored data, (Satten, G. A., Datta S. (2001). The Kaplan–Meier estimator as an inverse-probability-of-censoring weighted average. Amer. Statist. Ass. 55:207–210) showed that the Kaplan–Meier estimator (product-limit estimator (PLE)) can be expressed as an inverse-probability-weighted average. In this article, we consider the other two PLEs: the truncation PLE and the censoring-truncation PLE. For the data subject to left-truncation or both left-truncation and right-censoring, it is shown that these two PLEs can be expressed as inverse-probability-weighted averages. 相似文献
14.
AbstractIn this article, we propose a two folded approach for estimation of the population proportion of a sensitive attribute. The rationale of proposed technique is to give respondents choice if they want to avail randomized device or not. Thus, our technique is inherently capable of entertaining the responses attained through direct questioning and by employing randomization device, as well. We believe that free to choose policy will be helpful to develop a curtsy between interviewer and respondent (which is highly desirable, especially when sensitive issue is under consideration) and thus enhances the survey reliability. The proposed technique is developed for simple random sampling, at first, and then extended to stratified random sampling. The superior performance of proposed technique in comparison to the Kuk (1990) method is demonstrated throughout this article. We provide algebraic, graphical and numerical evidences in support of our proposed technique. Furthermore, we also offer cost analysis considering most commonly used cost functions in the literature of survey research. 相似文献
15.
In this article, we introduce a new two-parameter estimator by grafting the contraction estimator into the modified ridge estimator proposed by Swindel (1976). This new two-parameter estimator is a general estimator which includes the ordinary least squares, the ridge, the Liu, and the contraction estimators as special cases. Furthermore, by setting restrictions Rβ = r on the parameter values we introduce a new restricted two-parameter estimator which includes the well-known restricted least squares, the restricted ridge proposed by Groß (2003), the restricted contraction estimators, and a new restricted Liu estimator which we call the modified restricted Liu estimator different from the restricted Liu estimator proposed by Kaç?ranlar et al. (1999). We also obtain necessary and sufficient condition for the superiority of the new two-parameter estimator over the ordinary least squares estimator and the comparison of the new restricted two-parameter estimator to the new two-parameter estimator is done by the criterion of matrix mean square error. The estimators of the biasing parameters are given and a simulation study is done for the comparison as well as the determination of the biasing parameters. 相似文献
16.
AbstractIn this paper, a class of variance estimator is proposed of a finite population variance under an adaptive cluster sampling design in the presence of information on an auxiliary variable. We obtain expressions for the mean square error and bias for the developed estimators and their performance is evaluated on a Poisson clustered process and a real data set. The simulation study evaluates the efficiency of the suggested estimators for an adaptive cluster sampling (ACS) design and the Isaki (1983) estimator of the variance for SRSWOR over the sample variance for SRSWOR. 相似文献
17.
AbstractGrubbs and Weaver (1947) suggest a minimum-variance unbiased estimator for the population standard deviation of a normal random variable, where a random sample is drawn and a weighted sum of the ranges of subsamples is calculated. The optimal choice involves using as many subsamples of size eight as possible. They verified their results numerically for samples of size up to 100, and conjectured that their “rule of eights” is valid for all sample sizes. Here we examine the analogous problem where the underlying distribution is exponential and find that a “rule of fours” yields optimality and prove the result rigorously. 相似文献
18.
AbstractIn this paper, two bivariate models based on the proposed methods of Marshall and Olkin are introduced. In the first model, the new bivariate distribution is presented based on the proposed method of Marshall and Olkin (1967) which has natural interpretations, and it can be applied in fatal shock models or in competing risks models. In the second model, the proposed method of Marshall and Olkin (1997) is generalized to bivariate case and a new bivariate distribution is introduced. We call these new distributions as the bivariate Gompertz (BGP) distribution and bivariate Gompertz-geometric (BGPG) distribution, respectively. Moreover, the BGP model can be obtained as a special case of the BGPG model. Then, we present various properties of the new bivariate models. In this regard, the joint and conditional density functions, the joint cumulative distribution function can be obtained in compact forms. Also, the aging properties and the bivariate hazard gradient are discussed. This model has five unknown parameters and the maximum likelihood estimators cannot be obtained in explicit form. We propose to use the EM algorithm to compute the maximum likelihood estimators of the unknown parameters, and it is computationally quite tractable. Also, Monte Carlo simulations are performed to investigate the effectiveness of the proposed algorithm. Finally, we analyze three real data sets for illustrative purposes. 相似文献
19.
《统计学通讯:理论与方法》2013,42(10):2043-2052
Abstract Chiu [Chiu, S. N. (1999). An unbiased estimator for the survival function of censored data. Commun. Statist. - Theory Meth. 28(9):2249–2260.] proposed a nonparametric estimator for the survival function which is based on observable censoring times in the general censoring model. His estimator is less efficient than the Product-Limit estimator. Considering an informative censoring model this drawback can partially be overcome. This is shown by a nonparametric, uniformly consistent estimator based on observable censoring times within the simple Koziol–Green model. Some asymptotic properties of the new estimator are investigated and it is compared with the well-known ACL-estimator. 相似文献
20.
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