标题： 光滑回拟合在广义加性模型中 显示英文标题

标题： Smooth backfitting in generalized additive models

摘要： 广义可加模型在处理非高斯响应（包括二元数据和计数数据）的多元非参数回归中受到了统计学家和数据分析人员的欢迎。 本文提出了一种拟合广义可加模型的新似然方法。 该方法旨在最大化一个平滑似然函数。 通过求解一组非线性积分方程来估计可加函数。 基于牛顿-康托洛维奇定理，从平滑后拟合的角度发展出一种迭代算法。 讨论了估计量的渐近性质和算法的收敛性。 结果表明，我们提出的局部线性拟合方法达到了与使用其他组件知识的“oracle”估计器相同的偏差和方差。 还与最近提出的两阶段估计器[《Ann.Statist.》32 (2004) 2412--2443]进行了数值比较。 显示英文摘要

摘要： Generalized additive models have been popular among statisticians and data analysts in multivariate nonparametric regression with non-Gaussian responses including binary and count data. In this paper, a new likelihood approach for fitting generalized additive models is proposed. It aims to maximize a smoothed likelihood. The additive functions are estimated by solving a system of nonlinear integral equations. An iterative algorithm based on smooth backfitting is developed from the Newton--Kantorovich theorem. Asymptotic properties of the estimator and convergence of the algorithm are discussed. It is shown that our proposal based on local linear fit achieves the same bias and variance as the oracle estimator that uses knowledge of the other components. Numerical comparison with the recently proposed two-stage estimator [Ann. Statist. 32 (2004) 2412--2443] is also made.