共查询到20条相似文献,搜索用时 31 毫秒
1.
In this paper, the problem of estimating the scale matrix and their eigenvalues in a Wishart distribution and in a multivariate F distribution (which arise naturally from a two-sample setting) are considered. A new class of estimators which shrink the eigenvalues towards their arithmetic mean are proposed. It is shown that the new estimator which dominates the usual unbiased estimator under the squared error loss function. A simulation study was carried out to study the performance of these estimators. 相似文献
2.
Hirokazu Yanagihara 《Journal of multivariate analysis》2007,98(1):1-29
In this paper, we propose a new estimator for a kurtosis in a multivariate nonnormal linear regression model. Usually, an estimator is constructed from an arithmetic mean of the second power of the squared sample Mahalanobis distances between observations and their estimated values. The estimator gives an underestimation and has a large bias, even if the sample size is not small. We replace this squared distance with a transformed squared norm of the Studentized residual using a monotonic increasing function. Our proposed estimator is defined by an arithmetic mean of the second power of these squared transformed squared norms with a correction term and a tuning parameter. The correction term adjusts our estimator to an unbiased estimator under normality, and the tuning parameter controls the sizes of the squared norms of the residuals. The family of our estimators includes estimators based on ordinary least squares and predicted residuals. We verify that the bias of our new estimator is smaller than usual by constructing numerical experiments. 相似文献
3.
Dominique Fourdrinier William E. Strawderman 《Annals of the Institute of Statistical Mathematics》2003,55(4):803-816
We consider estimation of loss for generalized Bayes or pseudo-Bayes estimators of a multivariate normal mean vector, θ. In
3 and higher dimensions, the MLEX is UMVUE and minimax but is inadmissible. It is dominated by the James-Stein estimator and by many others. Johnstone (1988,
On inadmissibility of some unbiased estimates of loss,Statistical Decision Theory and Related Topics, IV (eds. S. S. Gupta and J. O. Berger), Vol. 1, 361–379, Springer, New York) considered the estimation of loss for the usual
estimatorX and the James-Stein estimator. He found improvements over the Stein unbiased estimator of risk. In this paper, for a generalized
Bayes point estimator of θ, we compare generalized Bayes estimators to unbiased estimators of loss. We find, somewhat surprisingly,
that the unbiased estimator often dominates the corresponding generalized Bayes estimator of loss for priors which give minimax
estimators in the original point estimation problem. In particular, we give a class of priors for which the generalized Bayes
estimator of θ is admissible and minimax but for which the unbiased estimator of loss dominates the generalized Bayes estimator
of loss. We also give a general inadmissibility result for a generalized Bayes estimator of loss.
Research supported by NSF Grant DMS-97-04524. 相似文献
4.
In this article, the problem of estimating the covariance matrix in general linear mixed models is considered. Two new classes of estimators obtained by shrinking the eigenvalues towards the origin and the arithmetic mean, respectively, are proposed. It is shown that these new estimators dominate the unbiased estimator under the squared error loss function. Finally, some simulation results to compare the performance of the proposed estimators with that of the unbiased estimator are reported. The simulation results indicate that these new shrinkage estimators provide a substantial improvement in risk under most situations. 相似文献
5.
Satoshi Kuriki 《Annals of the Institute of Statistical Mathematics》1993,45(4):731-739
The unbiased estimator of risk of the orthogonally invariant estimator of the skew-symmetric normal mean matrix is obtained, and a class of minimax estimators and their order-preserving modification are proposed. The estimators have applications in paired comparisons model. A Monte Carlo study to compare the risks of the estimators is given. 相似文献
6.
T. J. Rao 《Annals of the Institute of Statistical Mathematics》1981,33(1):225-231
Summary Murthy and Nanjamma [4] studied the problem of construction of almost unbiased ratio estimators for any sampling design using
the technique of interpenetrating subsamples. Subsequently, Rao [7], [8] has given a general method of constructing unbiased
ratio estimators by considering linear combinations of the two simple estimators based on the ratio of means and the mean
of ratios. However, it is difficult to choose an optimum weight (Rao [9]) which minimizes the variance of the combined estimator
since the weights are random in certain cases. In this note, we consider a different method of combining these estimators
and obtain a general class of almost unbiased ratio estimators of which Murthy and Nanjamma's is a particular case and derive
an optimum in this class. The case of simple random sampling where a similar class of almost unbiased ratio estimators can
be developed is briefly discussed. The results are illustrated by means of simple numerical examples. 相似文献
7.
Sadanori Konishi 《Annals of the Institute of Statistical Mathematics》1982,34(1):505-515
Summary Asymptotic properties of several estimators of interclass correlation from familial data are examined in the case of a variable
number of siblings per family. After showing that the usual sib-mean estimator is not consistent, a modified sib-mean estimator
is proposed. Asymptotic distributions of estimators are derived and a test procedure is provided for a certain testing problem
concerning interclass correlation. Several estimators are compared in the various mean number of siblings per family, using
asymptotic mean square errors.
The Institute of Statistical Mathematics 相似文献
8.
In practical survey sampling, nonresponse phenomenon is unavoidable. How to impute missing data is an important problem. There are several imputation methods in the literature. In this paper, the imputation method of the mean of ratios for missing data under uniform response is applied to the estimation of a finite population mean when the PPSWR sampling is used. The imputed estimator is valid under the corresponding response mechanism regardless of the model as well as under the ratio model regardless of the response mechanism. The approximately unbiased jackknife variance estimator is also presented. All of these results are extended to the case of non-uniform response. Simulation studies show the good performance of the proposed estimators. 相似文献
9.
James H Albert 《Journal of multivariate analysis》1981,11(3):400-417
In the simultaneous estimation of means from independent Poisson distributions, an estimator is developed which incorporates a prior mean and variance for each Poisson mean estimated. This estimator possesses substantially smaller risk than the usual estimator in a region of the parameter space and seems superior to other estimators proposed to estimate p Poisson means. It is indicated through two asymptotic results that, unlike the conjugate Bayes estimator, the risk of the estimator does not greatly exceed the risk of the usual estimator outside of the region of risk improvement. 相似文献
10.
Esra Akdeniz Duran Hongchang Hu 《Journal of Computational and Applied Mathematics》2011,235(5):1418-1428
In this paper we consider the semiparametric regression model, y=Xβ+f+ε. Recently, Hu [11] proposed ridge regression estimator in a semiparametric regression model. We introduce a Liu-type (combined ridge-Stein) estimator (LTE) in a semiparametric regression model. Firstly, Liu-type estimators of both β and f are attained without a restrained design matrix. Secondly, the LTE estimator of β is compared with the two-step estimator in terms of the mean square error. We describe the almost unbiased Liu-type estimator in semiparametric regression models. The almost unbiased Liu-type estimator is compared with the Liu-type estimator in terms of the mean squared error matrix. A numerical example is provided to show the performance of the estimators. 相似文献
11.
S.E. Ahmed 《随机分析与应用》2013,31(4):475-492
The simultaneous asymptotic estimation theory of quantiles is considered for an arbitrary population. The Stein–type estimator and its positive version are considered. The relative merits of the proposed estimators are compared with those of the usual estimator using asymptotic quadratic distributional risk those of the usual estimator using asymptotic quadratic distributional risk under local alternatives. It is shown that both proposed estimators are asymptotically superior to the classical estimator. Further, it is demonstrated that the Stein-type estimator is dominated by its positive part 相似文献
12.
A.M. Abd-Elfattah E.A. El-Sherpieny S.M. Mohamed O.F. Abdou 《Applied mathematics and computation》2010,215(12):4198-3099
This paper proposes some estimators for the population mean by adapting the estimator in Singh et al. (2008) [5] to the ratio estimators presented in Kadilar and Cingi 2006 [2]. We obtain mean square error (MSE) equation for all proposed estimators, and show that all proposed estimators are always more efficient than ratio estimator in Naik and Gupta (1996) [3], and Singh et al. (2008) [5]. The results have been illustrated numerically by taking some empirical population considered in the literature. 相似文献
13.
In this paper, the Bayes estimator and the parametric empirical Bayes estimator (PEBE) of mean vector in multivariate normal distribution are obtained. The superiority of the PEBE over the minimum variance unbiased estimator (MVUE) and a revised James-Stein estimators (RJSE) are investigated respectively under mean square error (MSE) criterion. Extensive simulations are conducted to show that performance of the PEBE is optimal among these three estimators under the MSE criterion. 相似文献
14.
考虑实际回归问题中存在更多受约束条件的情况,提出了带约束的统一几乎无偏估计类,统一了常见的具有线性约束的回归模型的几乎无偏估计,进一步的研究给出了在均方误差和均方误差矩阵意义下,带约束的统一几乎无偏估计优于一般带约束的最小二乘估计的充分条件和椭球范围. 相似文献
15.
研究了有限总体均值向量的无偏估计和线性可预测变量的无偏预测之间的关系,利用分块矩阵广义逆直接对加权风险函数进行分解,提出了一种由均值向量的无偏估计来构造无偏预测的新方法,并找到了它们之间的构造关系.特别地,线性可预测变量的最优线性无偏预测(BLUP)可由均值向量的最佳线性无偏估计(BLUE)惟一地表示(有关惟一性在几乎处处意义下理解). 相似文献
16.
Hironori Fujisawa 《Annals of the Institute of Statistical Mathematics》1996,48(3):423-428
The maximum likelihood estimators are uniquely obtained in a multivariate normal distribution with AR(1) covariance structure for monotone data. The maximum likelihood estimator of mean is unbiased. 相似文献
17.
Heinz Neudecker Roman Zmy?lony G?tz Trenkler 《International Journal of Mathematical Education in Science & Technology》2013,44(6):928-935
The problem of estimating the cross-product of two mean vectors in three-dimensional Euclidian space is considered. Two ‘natural’ estimators are developed, both of which turn out to be biased. A third, unbiased estimator, resulting from a jackknife procedure, is also investigated. It is shown that, under normality, the latter is best among all the unbiased estimators of this quantity. 相似文献
18.
19.
错误先验假定下Bayes线性无偏估计的稳健性 总被引:1,自引:0,他引:1
本文基于错误的先验假定获得了一般线性模型下可估函数的Bayes线性无偏估计(BLUE), 证明了在均方误差矩阵(MSEM)准则和后验Pitman Closeness (PPC)准则下BLUE相对于最小二乘估计(LSE)的优良性, 并导出了它们的相对效率的界, 从而获得BLUE的稳健性. 相似文献
20.
M. C. Agrawal 《Annals of the Institute of Statistical Mathematics》1984,36(1):323-335
Summary In this paper, we have undertaken an investigation covering three occasions in sampling on successive occasions with a view
to examining efficiency robustness of the best linear unbiased estimator (BLUE) visa-vis certain other potentially conceivable
estimators when the usual correlation model breaks down. We have inferred that the BLUE, is by and large, an efficiency robust
estimate in the face of unforeseen deviations from the usual correlation model. 相似文献