In this paper, we discuss the derivation of the first and second moments for the proposed small area estimators under a multivariate linear model for repeated measures data. The aim is to use these moments to estimate...
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In this paper, we discuss the derivation of the first and second moments for the proposed small area estimators under a multivariate linear model for repeated measures data. The aim is to use these moments to estimate the mean-squared errors (MSE) for the predicted small area means as a measure of precision. At the first stage, we derive the MSE when the covariance matrices are known. At the second stage, a method based on parametric bootstrap is proposed for bias correction and for prediction error that reflects the uncertainty when the unknown covariance is replaced by its suitable estimator.
In this article, we study the characterization of admissible linear estimators in a multivariate linear model with inequality constraint, under a matrix loss function. In the homogeneous class, we present several equi...
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In this article, we study the characterization of admissible linear estimators in a multivariate linear model with inequality constraint, under a matrix loss function. In the homogeneous class, we present several equivalent, necessary and sufficient conditions for a linear estimator of estimable functions to be admissible. In the inhomogeneous class, we find that the necessary and sufficient conditions depend on the rank of the matrix in the constraint. When the rank is greater than one, the necessary and sufficient conditions are obtained. When the rank is equal to one, we have necessary conditions and sufficient conditions separately. We also obtain the necessary and sufficient conditions for a linear estimator of inestimable function to be admissible in both classes.
In this article, small area estimation under a multivariate linear model for repeated measures data is considered. The proposed model aims to get a model which borrows strength both across small areas and over time. T...
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In this article, small area estimation under a multivariate linear model for repeated measures data is considered. The proposed model aims to get a model which borrows strength both across small areas and over time. The model accounts for repeated surveys, grouped response units, and random effects variations. Estimation of model parameters is discussed within a likelihood based approach. Prediction of random effects, small area means across time points, and per group units are derived. A parametric bootstrap method is proposed for estimating the mean squared error of the predicted small area means. Results are supported by a simulation study.
Ordinary least squares estimator (OLSE), best linear unbiased estimator (BLUE), and best linear unbiased predictor (BLUP) in the general linearmodel with new observations are generalized to the general multivariate l...
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Ordinary least squares estimator (OLSE), best linear unbiased estimator (BLUE), and best linear unbiased predictor (BLUP) in the general linearmodel with new observations are generalized to the general multivariate linear model. The fundamental equations of BLUE and BLUP in the multivariate linear model are derived by two methods, including the vectorization method and projection method. By using the matrix rank method, some new results of linear BLUE-sufficiency, linear BLUP-sufficiency, and the equality of OLSE, BLUE, and BLUP are given in the multivariate linear model.
We propose a class of robust estimates for multivariate linear models. Based on the approach of MM-estimation (Yohai 1987, [24]), we estimate the regression coefficients and the covariance matrix of the errors simulta...
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We propose a class of robust estimates for multivariate linear models. Based on the approach of MM-estimation (Yohai 1987, [24]), we estimate the regression coefficients and the covariance matrix of the errors simultaneously. These estimates have both a high breakdown point and high asymptotic efficiency under Gaussian errors. We prove consistency and asymptotic normality assuming errors with an elliptical distribution. We describe an iterative algorithm for the numerical calculation of these estimates. The advantages of the proposed estimates over their competitors are demonstrated through both simulated and real data. (C) 2011 Elsevier Inc. All rights reserved.
This paper deals with the likelihood ratio test for additional information in a multivariate linear model. It is shown that the power of the likelihood ratio test procedure has a monotonicity property. Asymptotic appr...
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This paper deals with the likelihood ratio test for additional information in a multivariate linear model. It is shown that the power of the likelihood ratio test procedure has a monotonicity property. Asymptotic approximations for the power are also obtained.
We consider a multivariate linear model with autocorrelated errors. The mean vector of the process is assumed to be linear in the time-trend parameter beta and the within-group variation parameter gamma. The least-squ...
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We consider a multivariate linear model with autocorrelated errors. The mean vector of the process is assumed to be linear in the time-trend parameter beta and the within-group variation parameter gamma. The least-squares estimators of beta and gamma, and the related estimators of the autoregressive parameter theta and the error covariance matrix SIGMA are derived and their asymptotic distributions are obtained. Large sample tests of H-1: gamma=0 and H-2: beta=0 are derived and the limit distributions of the restricted least-squares estimators beta(H1) and gamma(H2) are obtained under H-1 and H-2, respectively.
A Bayesian test procedure Is developed to test; the null hypothesis of no change In the regression matrix of a multivariate lin¬ear model against the alternative hypothesis of exactly one change The resulting tes...
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A Bayesian test procedure Is developed to test; the null hypothesis of no change In the regression matrix of a multivariate lin¬ear model against the alternative hypothesis of exactly one change The resulting test is based on the marginal posterior distribution of the change point; To illustrate the test procedure a numerical example using a bivariate regression model is considered.
This paper is concerned with consistency properties of rank estimation criteria in a multivariate linear model, based on the model selection criteria AIC, BIC and C-p. The consistency properties of these criteria are ...
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This paper is concerned with consistency properties of rank estimation criteria in a multivariate linear model, based on the model selection criteria AIC, BIC and C-p. The consistency properties of these criteria are studied under a high-dimensional framework with two different assumptions on the noncentrality matrix such that the number of response variables and the sample size tend to infinity. In general, it is known that under a large-sample asymptotic framework, the criteria based on AIC and C-p are not consistent, but the criterion based on BIC is consistent. However, we note that there are cases that the criteria based on AIC and C-p are consistent, but the criterion based on BIC is not consistent. Such consistency properties are also shown for the generalized criteria with a tuning parameter. Further, the modified criteria with a ridge-type estimator are also examined. Through a Monte Carlo simulation experiment, our results are checked numerically, and the estimation criteria are compared. (C) 2016 Elsevier Inc. All rights reserved.
In this paper we consider asymptotic approximations to the distribution function F(x) of a linear combination of an estimate in a multivariate linear model. A method is given for obtaining an asymptotic expansion Fs−1...
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In this paper we consider asymptotic approximations to the distribution function F(x) of a linear combination of an estimate in a multivariate linear model. A method is given for obtaining an asymptotic expansion Fs−1(x) of F(x) up to O(n−s+1) and a bound cs such that |F(x)−Fs−1(x)|≤cs uniformly in x and cs=O(n−s).
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