forward: Iterative bias reduction smoothing

Description

Performs a forward variable selection for iterative bias reduction using kernel or thin plate splines. In the latter case, the order m is chosen as the first integer such that 2m/d>1, where d is the number of explanatory variables. Missing values are not allowed.

Usage

forward(X, Y, criterion="gcv", df=1.5, Kmin=1, Kmax=10000, smoother="k", kernel="g",
 control.par=list(), cv.options=list(),varcrit=criterion)

Arguments

Value

Returns an object of class forwardibr which is a matrix with p columns. In the first row, each entry j contains the value of the chosen criterion for the univariate smoother using the jth explanatory variable. The variable which realize the minimum of the first row is included in the model. All the column of this variable will be Inf except the first row. In the second row, each entry j contains the bivariate smoother using the jth explanatory variable and the variable already included. The variable which realize the minimum of the second row is included in the model. All the column of this variable will be Inf except the two first row. This forward selection process continue until the chosen criterion increases.

References

Cornillon, P.-A.; Hengartner, N.; Jegou, N. and Matzner-Lober, E. (2012) Iterative bias reduction: a comparative study. Statistics and Computing. Doi: 10.1007/s11222-012-9346-4

Cornillon, P.-A.; Hengartner, N. and Matzner-Lober, E. (2013) Recursive bias estimation for multivariate regression smoothers Recursive bias estimation for multivariate regression smoothers. ESAIM: Probability and Statistics. Doi: http://dx.doi.org/10.1051/ps/2013046

Examples

Run this code

data(ozone, package = "ibr")
res.ibr <- forward(ozone[,-1],ozone[,1],df=1.2)
apply(res.ibr,1,which.min)