共查询到20条相似文献,搜索用时 15 毫秒
1.
Maciej Wilczyński 《Statistical Papers》2012,53(1):151-164
Arnold and Stahlecker (Stat Pap 44:107–115, 2003) considered the prediction of future values of the dependent variable in
the linear regression model with a relative squared error and deterministic disturbances. They found an explicit form for
a minimax linear affine solution d* of that problem. In the paper we generalize this result proving that the decision rule d* is also minimax when the class D{\mathcal{D}} of possible predictors of the dependent variable is unrestricted. Then we show that d* remains minimax in D{\mathcal{D}} when the disturbances are random with the mean vector zero and the known positive definite covariance matrix. 相似文献
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《Journal of statistical planning and inference》1997,62(2):301-316
In this paper, we derive the exact mean squared error (MSE) of the minimum MSE estimator for each individual coefficient in a linear regression model, and show a sufficient condition for the minimum MSE estimator for each individual coefficient to dominate the OLS estimator. Numerical results show that when the number of independent variables is 2 and 3, the minimum MSE estimator for each individual coefficient can be a good alternative to the OLS and Stein-rule estimators. 相似文献
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《Journal of statistical planning and inference》1996,50(1):77-89
Estimationof the coefficient vector of a linear regression model subject to ellipsoidal constraints on the coefficients has been considered. Shrinkage methodology has been synthesized with minimax estimation technique and an estimator based on this has been proposed. The properties of this estimator have been derived under a quadratic loss set-up of the decision theory which are analysed to assess the behaviour of the proposed estimator. Superiority conditions for the dominance of this estimator over the existing minimax and least-squares estimators have also been derived. 相似文献
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In linear regression models, predictors based on least squares or on generalized least squares estimators are usually applied
which, however, fail in case of multicollinearity. As an alternative biased estimators like ridge estimators, Kuks-Olman estimators,
Bayes or minimax estimators are sometimes suggested. In our analysis the relative instead of the generally used absolute squared
error enters the objective function. An explicit minimax solution is derived which, in an important special case, can be viewed
as a predictor based on a Kuks-Olman estimator. 相似文献
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A maximum likelihood solution is presented for analyzing data which arise from a linear model whose error term is assumed to have variance proportional to some unknown power of the response. An efficient iterative method for solving the likelihood equations is obtained which incoporates use of a transfomation to orthogonalize the two variance paramaters. Assessments of the method are made through simulations study and the results are compared with those of the ordinary least squares. Examples from the literature are included to illustrate the method and also to compare the results with a weighted least squares estimates. 相似文献
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In order to obtain optimal estimators in a generalized linear regression model we apply the minimax principle to the relative squared error. It turns out that this approach is equivalent to the application of the minimax principle to the absolute squared error when an ellipsoidal prior information set is given. We discuss the admissibility of these minimax estimators. Furthermore, a close relation to a Bayesian approach is derived. 相似文献
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In this article, we propose a version of a kernel density estimator which reduces the mean squared error of the existing kernel density estimator by combining bias reduction and variance reduction techniques. Its theoretical properties are investigated, and a Monte Carlo simulation study supporting theoretical results on the proposed estimator is given. 相似文献
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J. Michael Steele 《Revue canadienne de statistique》1978,6(2):193-200
The average squared error has been suggested earlier as an appropriate estimate of the integrated squared error, but an example is given which shows their ratio can tend to infinity. The results of a Monte Carlo study are also presented which suggest the average squared error can seriously underestimate the errors inherent in even the simplest density estimations. 相似文献
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In this paper we analyze the properties of two estimators oroposed by Farebrother (1975) for linear regression models. 相似文献
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Richard Valliant 《统计学通讯:理论与方法》2013,42(6):1975-1993
Four estimators of the prediction mean squared error (MSB) of an estimated finite population total for a zero-one characteristic are examined. The characteristic associated with each population unit is modeled as the realization of a Bernoulli random variable whose expected value is a nonlinear function of a parameter vector and a set of known auxiliary variables. To compare the estimators, a simulation study is conducted using a population of hospitals. The MSB estimator Implied by the form of the assumed model underestimates the mean squared error in each of the cases studied and produces confidence lntervals with less than the nominal coverage probabilities. Of the three alternative MSE estimators presented, a linear approximation to the jackknife produces the best results and improves upon the model-specific estimator. 相似文献
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Two families of parameter estimation procedures for the stable laws based on a variant of the characteristic function are provided. The methodology which produces viable computational procedures for the stable laws is generally applicable to other families of distributions across a variety of settings. Both families of procedures may be described as a modified weighted chi-squared minimization procedure, and both explicitly take account of constraints on the parameter space. Influence func-tions for and efficiencies of the estimators are given. If x1, x2, …xn random sample from an unknown distribution F , a method for determining the stable law to which F is attracted is developed. Procedures for regression and autoregres-sion with stable error structure are provided. A number of examples are given. 相似文献
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Samuel Gutmann 《统计学通讯:理论与方法》2013,42(18):2075-2082
The minimax linear Empirical Bayes estimators for a binomial parameter are obtained, assuming some information about the moments of the prior. The form of these estimates is used to propose a criterion which may be helpful in determining whether Empirical Bayes estimation is Indicated for a given problem. 相似文献
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ABSTRACTAs an alternative to the functional quadratic model due to Yao and Müller (2010), we consider a functional quadratic multiplicative model. This multiplicative model provides a useful alternative when the relative error is considered for analyzing data with positive responses. The existing work for functional models are mainly based on absolute errors. The commonly used least squares criterion is just such an example. In many practical applications, however, people concern on the size of relative error rather than that of error itself. Therefore, the estimation procedure based on least absolute relative errors, which is proposed by Chen et al. (2010) for the linear multiplicative model, is developed for functional quadratic multiplicative model. The asymptotic behaviors of the proposed estimators are established. Some simulation studies show that the estimation procedure has good prediction performance. Moreover, a real data set is analyzed for illustrating the proposed methods. 相似文献
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Peter J. Kempthorne 《统计学通讯:理论与方法》2013,42(7):2145-2157
Minimax squared error risk estimators of the mean of a multivariate normal distribution are characterized which have smallest Bayes risk with respect to a spherically symmetric prior distribution for (i) squared error loss, and (ii) zero-one loss depending on whether or not estimates are consistent with the hypothesis that the mean is null. In (i), the optimal estimators are the usual Bayes estimators for prior distributions with special structure. In (ii), preliminary test estimators are optimal. The results are obtained by applying the theory of minimax-Bayes-compromise decision problems. 相似文献
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This paper is concerned with prediction in the spatial linear model using the maximum likelihood estimation of parameters in this model. In particular, we give some properties of predictors obtained on substituting the maximum likelihood estimators of model parameters into the form of the best-in the sense of minimum mean square prediction error-predictor. Such predictors are not optimal but we show them to be asymptotically equivalent to the optimum. We discuss practical aspects of this work and conclude by considering the connection with other areas. 相似文献