Smooth backfitting in practice

• Published in: Journal of the Royal Statistical Society. Series B, Statistical methodology Vol. 67; no. 1; pp. 43 - 61
• Main Authors: Nielsen, Jens Perch, Sperlich, Stefan
• Format: Journal Article
• Language: English
• Published: Oxford, UK Blackwell Publishing 01.02.2005; Blackwell Publishers; Blackwell; Royal Statistical Society; Oxford University Press
• Series: Journal of the Royal Statistical Society Series B
• Subjects: Additivity; Asymptotic methods; Backfitting; Bandwidth choice; Computational statistics; Cross-validation; Data smoothing; Economic models; Error rates; Estimating techniques; Estimation bias; Estimation methods; Estimators; Exact sciences and technology; Mathematical methods; Mathematical procedures; Mathematics; Modeling; Nonparametric estimation; Nonparametric inference; Practice; Probability and statistics; Sample size; Sciences and techniques of general use; Simulation; Statistical methods; Statistics; Studies; Statistical method; Fitting; Correlation analysis; Experimental design; Bandwith selection; Non parametric estimation; Cross validation; Asymptotic approximation
• ISSN: 1369-7412; 1467-9868
• DOI: 10.1111/j.1467-9868.2005.00487.x

Compared with the classical backfitting of Buja, Hastie and Tibshirani, the smooth backfitting estimator (SBE) of Mammen, Linton and Nielsen not only provides complete asymptotic theory under weaker conditions but is also more efficient, robust and easier to calculate. However, the original paper describing the SBE method is complex and the practical as well as the theoretical advantages of the method have still neither been recognized nor accepted by the statistical community. We focus on a clear presentation of the idea, the main theoretical results and practical aspects like implementation and simplification of the algorithm. We introduce a feasible cross-validation procedure and apply it to the problem of data-driven bandwidth choice for the SBE. By simulations it is shown that the SBE and our cross-validation work very well indeed. In particular, the SBE is less affected by sparseness of data in high dimensional regression problems or strongly correlated designs. The SBE has reasonable performance even in 100-dimensional additive regression problems.