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Zbl 0765.62064
Friedman, Jerome H.
Multivariate adaptive regression splines. (English)
[J] Ann. Stat. 19, No.1, 1-141 (1991). ISSN 0090-5364

Summary: A new method is presented for flexible regression modeling of high dimensional data. The model takes the form of an expansion in product spline basis functions, where the number of basis functions as well as the parameters associated with each one (product degree and knot locations) are automatically determined by the data.\par This procedure is motivated by the recursive partitioning approach to regression and shares its attractive properties. Unlike recursive partitioning, however, this method produces continuous models with continuous derivatives. It has more power and flexibility to model relationships that are nearly additive or involve interactions in at most a few variables. In addition, the model can be represented in a form that separately identifies the additive contributions and those associated with the different multivariable interactions.

MSC 2000:: *62J02 General nonlinear regression
62H99 Multivariate analysis
65D10 Smoothing
65D07 Splines (numerical methods)
65C99 Numerical simulation

Keywords: nonparametric multiple regression; multivariable function approximation; statistical learning neural networks; multivariate smoothing; AID; CART; product degree; high dimensional data; expansion in product spline basis functions; knot locations; recursive partitioning approach to regression; continuous models; continuous derivatives

Cited in: Zbl 1048.62061 Zbl 1092.62089 Zbl 0986.62031 Zbl 1059.62668 Zbl 0824.62033 Zbl 0795.62057

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