backf.rob {RBF}

Robust Backfitting

Description

This function computes a robust backfitting algorithm for additive models

Usage

backf.rob(
  formula,
  data,
  subset,
  windows,
  point = NULL,
  epsilon = 1e-06,
  degree = 0,
  sigma.hat = NULL,
  prob = NULL,
  max.it = 50,
  k.h = 1.345,
  k.t = 4.685,
  type = "Huber"
)

Arguments

formula

an object of class formula (or one that can be coerced to that class): a symbolic description of the model to be fitted.

data

an optional data frame, list or environment (or object coercible by as.data.frame to a data frame) containing the variables in the model. If not found in data, the variables are taken from environment(formula), typically the environment from which the function was called.

subset

an optional vector specifying a subset of observations to be used in the fitting process.

windows

vector of bandwidths for the local polynomial smoother, one per explanatory variable.

point

matrix of points where predictions will be computed and returned.

epsilon

convergence criterion. Maximum allowed relative difference between consecutive estimates

degree

degree of the local polynomial smoother. Defaults to 0 (local constant).

sigma.hat

estimate of the residual standard error. If NULL (default) we use the mad of the residuals obtained with local medians.

prob

vector of probabilities of observing each response (length n). Defaults to NULL and in that case it is ignored.

max.it

Maximum number of iterations for the algorithm.

k.h

tuning constant for a Huber-type loss function.

k.t

tuning constant for a Tukey-type loss function.

type

one of either 'Tukey' or 'Huber'.

Details

This function computes a robust backfitting algorithm for additive models using robust local polynomial smoothers.

Value

A list with the following components:

alpha

Estimate for the intercept.

g.matrix

Matrix of estimated additive components (n by p).

prediction

Matrix of estimated additive components for the points listed in the argument point.

sigma.hat

Estimate of the residual standard error.

Author(s)

Matias Salibian-Barrera, [e-mail], Alejandra Martinez

References

Boente G, Martinez A, Salibian-Barrera M. Robust estimators for additive models using backfitting. Journal of Nonparametric Statistics, 2017; 29:744-767. https://doi.org/10.1080/10485252.2017.1369077

Examples

data(airquality)
tmp <- backf.rob(Ozone ~ Solar.R + Wind + Temp, data=airquality, 
subset=complete.cases(airquality), windows=c(136.7, 8.9, 4.8), degree=1)