An asymptotic theory for weighted least-squares with weights estimated by replication
An asymptotic theory for weighted least-squares with weights estimated by replication
复制标题
权重通过复制估计的加权最小二乘渐近理论
DOI：
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发表时间：
1988
期刊：
影响因子：
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通讯作者：
D. Cline
中科院分区：
文献类型：
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作者：
R. Carroll;D. Cline
摘要我们考虑了一个带复制项的异方差线性回归模型。要估计方差，可以使用回归拟合的样本方差或样本平均平方误差。我们研究了这些加权最小二乘估计与估计的权重时，重复的数量是小的大样本性质。对于非对称分布的数据，估计值通常不一致。如果基于m个重复样本使用样本方差，则即使数据呈正态分布，m =2个重复样本的加权最小二乘估计值也不一致。在3到5次重复的情况下，收敛速度比通常的N的平方根慢。对于m - 6个重复样本，相对于已知权重的加权最小二乘估计值，估计权重的效果是使方差增加（m - 5）/（m-3）。
SUMMARY We consider a heteroscedastic linear regression model with replication. To estimate the variances, one can use the sample variances or the sample average squared errors from a regression fit. We study the large-sample properties of these weighted least-squares estimates with estimated weights when the number of replicates is small. The estimates are generally inconsistent for asymmetrically distributed data. If sample variances are used based on m replicates, the weighted least-squares estimates are inconsistent for m =2 replicates even when the data are normally distributed. With between 3 and 5 replicates, the rates of convergence are slower than the usual square root of N. With m - 6 replicates, the effect of estimating the weights is to increase variances by (m - 5)/(m -3), relative to weighted least-squares estimates with known weights.