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Bio-Design and Manufacturing  2018 Vol.1 No.1 P.71-77

10.1631/jzus.2000.0071


ESTIMATION METHOD FOR MIXED-EFFECT COEFFICIENT SEMIPARAMETRIC REGRESSION MODEL


Author(s):  PAN Jian-min

Affiliation(s):  Department of Mathematics, Xixi Campus of Zhejiang University, Hangzhou 310028, China

Corresponding email(s): 

Key Words:  mixed-effect coefficient, semiparametric regression model, the nearest neighbor estimation, asymptotic normality, the best convergence rate


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PAN Jian-min. ESTIMATION METHOD FOR MIXED-EFFECT COEFFICIENT SEMIPARAMETRIC REGRESSION MODEL[J]. Journal of Zhejiang University Science D, 2018, 1(1): 71-77.

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Abstract: 
Consider the mixed-effect coefficient semiparametric regression model Z=X'α+Y'β+g(T)+e, where X, Y and T are random vectors on Rp×Rq×[0,1], α is a p-dimensional fixed-effect parameter, β is a q-dimensional random-effect parameter (Eβ=b, Cov(β)=∑), g(.) is an unknown function on [0,1], e is a random error with mean zero and variance σ2, and (X,Y,T) and (β,e), β and e are mutually independent. We estimate α, b and g(.) by the nearest neighbor and the least square method. In this paper, we prove that estimations of α, b have asymptotic normality and obtain the best convergence rate n−1/3 for the estimation of g(.).

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Reference

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