A note on the backfitting estimation of additive models

作者：Xia Yingcun^*

来源：Bernoulli, 2009, 15(4): 1148-1153.

DOI：10.3150/09-BEJ183

• additive model
• backfitting algorithm
• convergence of algorithm
• kernel smoothing

The additive model is one of the most popular semi-parametric models The backfitting estimation (Buja, Hastie and Tibshiram. Ann Statist 17 (1989) 453-555) for the model IS Intuitively easy to understand and theoretically most efficient (Opsomer and Ruppert, Ann Statist 25 (1997) 186-211), 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 (Ann Statist 25 (1997) 186-211) proved the convergence under a very strong condition and conjectured that a much weaker condition is sufficient In this short note, we show that I weak condition can guarantee the convergence of the backfitting estimation algorithm when Nadaraya-Watson kernel Smoothing is used

• 出版日期2009-11