Nonparametric Regression Estimation using Weak Separability
Nonparametric Regression Estimation using Weak Separability
复制标题
使用弱可分离性的非参数回归估计
DOI：
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发表时间：
2001
期刊：
影响因子：
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通讯作者：
M. Slade
中科院分区：
文献类型：
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作者：
J. Pinkse;John W. Galbraith;D. Green;N. Heckman;J. Horowitz;Oliver Linton;Rosa L. Matzkin;P. Robinson;M. Slade
本文提出了弱可分性条件下非参数回归函数的三个新估计。WS的使用减少了维数灾难。WS嵌套其他可分性概念，如（广义）加法可分性（（G）AS）。WS优于（G）AS的优点是WS允许回归变量之间的相互作用，而（G）AS不允许任何相互作用。估计使用边际积分，并示出具有限制正态分布和收敛速度，这是相同的无约束的非参数估计的回归函数的低维。我的两个估计量的一个吸引人的和不寻常的特点是，回归可以有任意凸支持和积分区域可以依赖于其余变量的值。估计可以迭代，我表明，在强有力的假设下，进一步提高渐近效率是可能的。估计量的计算是简单的。在模拟研究的估计之一的性能进行了研究。
In this paper I propose three new estimators of nonparametric regression functions subject to weak separability (WS). The use of WS reduces the curse of dimensionality. WS nests other separability concepts such as (generalized) additive separability ((G)AS). The advantage of WS over (G)AS is that WS allows for interactions between regressors whereas (G)AS does not permit any interactions. The estimators use marginal integration and are shown to have a limiting normal distribution and a convergence rate which is the same as that of an unconstrained nonparametric estimator of a regression function of lower dimension. An attractive and unusual feature of two of my estimators is that regressors can have arbitrary convex support and that the integration regions can depend on the values of the remaining variables. The estimators can be iterated and I show that under strong assumptions further asymptotic efficiency improvements are possible. The computation of the estimators is simple. The performance of one of the estimators is studied in a simulation study.