Bias reduction in kernel binary regression
Bias reduction in kernel binary regression
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DOI：
10.1016/j.csda.2006.06.012
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发表时间：
2007-05-15
影响因子：
1.8
通讯作者：
Hazelton, Martin L.
中科院分区：
文献类型：
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作者：
Hazelton, Martin L.
我们考虑二元回归函数的Nadaraya-Watson型估计。我们提出了一种方法，用于提高这种估计的性能，采用偏差减少技术时，估计的成分概率密度。在实际应用中，将单独优化的密度估计直接代入回归函数公式会产生令人失望的结果。然而，调整全局平滑参数来优化二元回归函数本身的性能标准更有希望。我们专注于这种方法的实现，它使用一个可变的内核技术，以提供减少的偏差密度估计，并在全球带宽选择适当量身定制的留一法（交叉验证）。理论和数值实验表明，这种形式的偏差减少大大提高了性能时，基本的回归函数是高度非线性的，但不是有益的，当基本的回归函数几乎是线性的形式。(c)2006 Elsevier B. V.保留所有权利。
We consider Nadaraya-Watson type estimators for binary regression functions. We propose a method for improving the performance of such estimators by employing bias reduction techniques when estimating the constituent probability densities. Direct substitution of separately optimized density estimates into the regression function formula generates disappointing results in practice. However, adjusting the global smoothing parameter to optimize a performance criterion for the binary regression function itself is more promising. We focus on an implementation of this approach which uses a variable kernel technique to provide reduced bias density estimates, and where the global bandwidth is selected by an appropriately tailored leave-one-out (cross-validation) method. Theory and numerical experiments show that this form of bias reduction improves performance substantially when the underlying regression function is highly non-linear but is not beneficial when the underlying regression function is almost linear in form. (c) 2006 Elsevier B.V. All rights reserved.