On Deconvolution as a First Stage Nonparametric Estimator
On Deconvolution as a First Stage Nonparametric Estimator
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关于反卷积作为第一阶段非参数估计器
DOI：
10.1080/07474930903559276
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发表时间：
2005
影响因子：
1.2
通讯作者：
G. Ridder
中科院分区：
文献类型：
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作者：
Yingyao Hu;G. Ridder
我们重新考虑 Taupin (2001) 的积分非线性回归 (INLR) 估计器，用于具有误测协变量的非线性回归。我们发现，如果我们将测量误差的分布限制为一类支持受限的分布，那么比她的平滑度假设弱得多的平滑度假设就足以确保估计量的一致性。此外，我们还表明，如果测量误差分布的支持随着样本大小的增加而扩展，则 INLR 估计量在这些较弱平滑度假设下保持一致。在这种情况下，估计量也保持渐近正态，收敛速度任意接近 。我们的结果表明，反卷积可以用于非参数第一步，而无需对参数模型施加限制性平滑假设。
We reconsider Taupin's (2001) Integrated Nonlinear Regression (INLR) estimator for a nonlinear regression with a mismeasured covariate. We find that if we restrict the distribution of the measurement error to a class of distributions with restricted support, then much weaker smoothness assumptions than hers suffice to ensure consistency of the estimator. In addition, we show that the INLR estimator remains consistent under these weaker smoothness assumptions if the support of the measurement error distribution expands with the sample size. In that case the estimator remains also asymptotically normal with a rate of convergence that is arbitrarily close to . Our results show that deconvolution can be used in a nonparametric first step without imposing restrictive smoothness assumptions on the parametric model.