应用概率统计
應用概率統計
응용개솔통계
CHINESE JOURNAL OF APPLIED PROBABILITY AND STATISTICS
2006年
3期
245-251
,共7页
变系数混合效应模型%局部多项式%渐进正态性%相合性
變繫數混閤效應模型%跼部多項式%漸進正態性%相閤性
변계수혼합효응모형%국부다항식%점진정태성%상합성
Varying coeffificient mixed-effects model%local polynomial%asymptotic normality%consistency
本文研究了下列变系数混合效应模型:yij=zτijbi+xτijβ(wij)+εij,i=1,…,m;j=1,…,ni,其中bi为i.i.d.期望为θ,协方差阵为σ2BIq的随机效应向量,εij是i.i.d.期望为零,具有有限方差的随机误差.文中我们不仅给出了函数系数向量β(·)的局部多项式估计,同时给出了随机效应期望、方差和随机误差方差的估计,并给出了这些估计量的渐进正态性和相合性,研究结果表明了这些估计量的可靠性.
本文研究瞭下列變繫數混閤效應模型:yij=zτijbi+xτijβ(wij)+εij,i=1,…,m;j=1,…,ni,其中bi為i.i.d.期望為θ,協方差陣為σ2BIq的隨機效應嚮量,εij是i.i.d.期望為零,具有有限方差的隨機誤差.文中我們不僅給齣瞭函數繫數嚮量β(·)的跼部多項式估計,同時給齣瞭隨機效應期望、方差和隨機誤差方差的估計,併給齣瞭這些估計量的漸進正態性和相閤性,研究結果錶明瞭這些估計量的可靠性.
본문연구료하렬변계수혼합효응모형:yij=zτijbi+xτijβ(wij)+εij,i=1,…,m;j=1,…,ni,기중bi위i.i.d.기망위θ,협방차진위σ2BIq적수궤효응향량,εij시i.i.d.기망위령,구유유한방차적수궤오차.문중아문불부급출료함수계수향량β(·)적국부다항식고계,동시급출료수궤효응기망、방차화수궤오차방차적고계,병급출료저사고계량적점진정태성화상합성,연구결과표명료저사고계량적가고성.
In this paper we consider the following varying coefficient mixed-effects model: yij = zτijbi+xτijβ(wij) + εij, i = 1,… ,m; j = 1,… ,ni, where bi is i.i.d. random effects with mean vector θ and covariance matrix σ2bIq, εij is i.i.d. random errors with zero mean and finite variance.The local polynomial estimator of the function coefficient vector β(·) is proposed. The method for estimating the mean of random effects, variances of random effects and random errors are also given. Asymptotic normality and consistency for the estimators are established, which give useful insight into the reliability of these general estimation methods.