Fitting a Bivariate Additive Model by Local Polynomial Regression
Fitting a Bivariate Additive Model by Local Polynomial Regression
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DOI：
10.1214/aos/1034276626
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发表时间：
1997-03
影响因子：
4.5
通讯作者：
J. Opsomer;D. Ruppert
中科院分区：
文献类型：
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作者：
J. Opsomer;D. Ruppert
虽然加性模型是一种流行的非参数回归方法，但它的许多理论性质尚未得到很好的理解，特别是当使用反拟合算法计算估计量时。本文探讨了用局部多项式回归拟合加性模型时的这些性质。给出了二元加性模型唯一估计量渐近存在的充分条件。本文计算了具有奇数次和偶数次局部多项式项的同方差二元加性模型的偏差和方差的渐近逼近。该模型具有与单变量局部多项式回归相同的收敛速度。
While the additive model is a popular nonparametric regression method, many of its theoretical properties are not well understood, especially when the backfitting algorithm is used for computation of the estimators. This article explores those properties when the additive model is fitted by local polynomial regression. Sufficient conditions guaranteeing the asymptotic existence of unique estimators for the bivariate additive model are given. Asymptotic approximations to the bias and the variance of a homoscedastic bivariate additive model with local polynomial terms of odd and even degree are computed. This model is shown to have the same rate of convergence as that of univariate local polynomial regression.