R: Robust Backfitting

backf.rob {RBF} | R Documentation

## 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, matias@stat.ubc.ca, 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)

[Package RBF version 2.0.1 Index]