关于可加模型回拟估计的一个注记
A Note on The Backfitting Estimation of Additive Models
摘要：
可加性模型是最常用的半参数模型之一。模型的后拟合估计（Buja，Hastie和Tibshirani，1989，\textit{Ann. Statist.}）直观上易于理解，理论上最有效（Opsomer和Ruppert，1997，\textit{Ann. Statist.}）;其实现等同于求解简单的线性方程。然而，该算法的收敛性是非常困难的调查，仍然是未解决的。对于二元可加模型，Opsomer和Ruppert（1997，\textit{Ann. Statist.}）在一个很强的条件下证明了收敛性，并证明了一个更弱的条件是充分的。在这篇短文中，我们证明了一个弱条件可以保证使用Nadaraya-Watson核平滑时的后拟合估计算法的收敛性。
英文摘要：
The additive model is one of the most popular semiparametric models. The backfitting estimation (Buja, Hastie and Tibshirani, 1989, \textit{Ann. Statist.}) for the model is intuitively easy to understand and theoretically most efficient (Opsomer and Ruppert, 1997, \textit{Ann. Statist.}); its implementation is equivalent to solving simple linear equations. However, convergence of the algorithm is very difficult to investigate and is still unsolved. For bivariate additive models, Opsomer and Ruppert (1997, \textit{Ann. Statist.}) proved the convergence under a very strong condition and conjectured that a much weaker condition is sufficient. In this short note, we show that a weak condition can guarantee the convergence of the backfitting estimation algorithm when the Nadaraya-Watson kernel smoothing is used.
机构、总结、中文摘要均由AI分析而来，可能存在错误，请以论文正文为准。
