WEIGHTED LIKELIHOOD ESTIMATION UNDER TWO-PHASE SAMPLING.
WEIGHTED LIKELIHOOD ESTIMATION UNDER TWO-PHASE SAMPLING.
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DOI：
10.1214/12-aos1073
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发表时间：
2013-02-01
影响因子：
4.5
通讯作者：
Wellner JA
中科院分区：
文献类型：
--
作者：
Saegusa T;Wellner JA
本文研究了无替换两阶段分层抽样下加权似然估计的渐近理论。我们还考虑了几个变种的WLE涉及估计的权重和校准。一组经验过程工具的开发，包括一个Glivenko-Cantelli定理，M-估计的收敛速度定理，和一个Donsker定理的逆概率加权经验过程下的两阶段抽样和抽样没有更换在第二阶段。使用这些一般的结果，我们推导出渐近分布的WLE的一个有限维参数在一般的半参数模型的滋扰参数的估计是可估计的定期或非定期率。我们在右删失和区间删失的考克斯模型中说明了这些结果和方法。我们比较的方法，通过他们的渐近方差下的抽样没有更换和更常见的（和更容易分析）的假设伯努利抽样在第二阶段。
We develop asymptotic theory for weighted likelihood estimators (WLE) under two-phase stratified sampling without replacement. We also consider several variants of WLEs involving estimated weights and calibration. A set of empirical process tools are developed including a Glivenko–Cantelli theorem, a theorem for rates of convergence of M-estimators, and a Donsker theorem for the inverse probability weighted empirical processes under two-phase sampling and sampling without replacement at the second phase. Using these general results, we derive asymptotic distributions of the WLE of a finite-dimensional parameter in a general semiparametric model where an estimator of a nuisance parameter is estimable either at regular or nonregular rates. We illustrate these results and methods in the Cox model with right censoring and interval censoring. We compare the methods via their asymptotic variances under both sampling without replacement and the more usual (and easier to analyze) assumption of Bernoulli sampling at the second phase.