【摘 要】
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Let Y =∑ki=1 XiθiZ(1)i +ε be the extended growth curve model with ε distributed with mean 0 and covariance In (O) Σ where Y is an n × p matrix of obse
【机 构】
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Department of Statistics, Shanghai University of Finance and Economics
【出 处】
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IMS-China International Conference on Statistics and Probabi
论文部分内容阅读
Let Y =∑ki=1 XiθiZ(1)i +ε be the extended growth curve model with ε distributed with mean 0 and covariance In (O) Σ where Y is an n × p matrix of observations,θi, Σunknown matrices of parameters and Xi, Zi known design matrices of the full rank.In this paper, the two-stage generalized least squares estimators (O)i(Y)s for the first order parameter θis are investigated and proved to be consistent as the sample size n tends to in?nity.Further, the asymptotic distributions of all (O)i(Y)s are obtained under the conditions that lim n→∞X(1)i(I-PXi+1)Xi/n =Ri for a positive definite matrix Ri for i =1,…, k.In addition, an unbiased and invariant quadratic estimator (∑)(Y) is also proved to be consistent to the second order parameter matrix.
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