Estimating equations with nuisance parameters: Theory and applications
Estimating equations with nuisance parameters: Theory and applications
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DOI：
10.1023/a:1004122007440
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发表时间：
2000-06-01
影响因子：
1
通讯作者：
Jennrich, RI
中科院分区：
文献类型：
--
作者：
Yuan, KH;Jennrich, RI
在各种统计问题中，参数 theta 的估计值 (n) 被定义为广义估计方程 G(n)((n), (n)) = 0 的根，其中 (n) 是干扰参数 gamma 的估计值。我们给出以这种方式定义的 (n) 的渐近正态性的充分条件，并推导出它们的渐近分布。 A. 注意到(n)的渐近分布不会受到(n)的渐近分布影响的情况。作为一个例子，我们考虑协方差结构分析，其中总体均值和总体四阶矩都是干扰参数。简要讨论了伪最大似然、具有估计权重的广义最小二乘法以及具有估计尺度参数的 M 估计的应用。
In a variety of statistical problems the estimate (n), of a parameter theta is defined as the root of a generalized estimating equation G(n)((n), (n)) = 0 where (n) is an estimate of a nuisance parameter gamma. We give sufficient conditions for the asymptotic normality of (n), defined in this way and derive their asymptotic distribution. A. circumstance under which the asymptotic distribution of (n), will not be influenced by that of (n) is noted. As an example, we consider a covariance structure analysis in which both the population mean and the population fourth-order moment are nuisance parameters. Applications to pseudo maximum likelihood, generalized least squares with estimated weights, and M-estimation with an estimated scale parameter are discussed briefly.