R: Robust marginal integration procedures for additive models

margint.rob

R Documentation

Robust marginal integration procedures for additive models

Description

This function computes robust marginal integration procedures for additive models.

Usage

margint.rob(
  formula,
  data,
  subset,
  point = NULL,
  windows,
  prob = NULL,
  sigma.hat = NULL,
  win.sigma = NULL,
  epsilon = 1e-06,
  type = "0",
  degree = NULL,
  typePhi = "Huber",
  k.h = 1.345,
  k.t = 4.685,
  max.it = 20,
  qderivate = FALSE,
  orderkernel = 2,
  Qmeasure = NULL
)

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.
`point`	a matrix of points where predictions will be computed and returned.
`windows`	a vector or a squared matrix of bandwidths for the smoothing estimation procedure.
`prob`	a vector of probabilities of observing each response (n). Defaults to `NULL`.
`sigma.hat`	estimate of the residual standard error. If `NULL` we use the mad of the residuals obtained with local medians.
`win.sigma`	a vector of bandwidths for estimating sigma.hat. If `NULL` it uses the argument windows if it is a vector or its diagonal if it is a matrix.
`epsilon`	convergence criterion.
`type`	three different type of estimators can be selected: type `'0'` (local constant on all the covariates), type `'1'` (local linear smoother on all the covariates), type `'alpha'` (local polynomial smoother only on the direction of interest).
`degree`	degree of the local polynomial smoother in the direction of interest when using the estimator of type `'alpha'`. Defaults to `NULL` for the case when using estimators of type `'0'` or `'1'`.
`typePhi`	one of either `'Tukey'` or `'Huber'`.
`k.h`	tuning constant for a Huber-type loss function. Defaults to `1.345`.
`k.t`	tuning constant for a Tukey-type loss function. Defaults to `4.685`.
`max.it`	maximum number of iterations for the algorithm.
`qderivate`	if TRUE, it calculates `g^(q+1)/(q+1)!` for each component only for the type `'alpha'` method. Defaults to `FALSE`.
`orderkernel`	order of the kernel used in the nuisance directions when using the estimator of type `'alpha'`. Defaults to `2`.
`Qmeasure`	a matrix of points where the integration procedure ocurrs. Defaults to `NULL` for calcuting the integrals over the sample.

Details

This function computes three types of robust marginal integration procedures for additive models.

Value

A list with the following components:

`mu`	Estimate for the intercept.
`g.matrix`	Matrix of estimated additive components (n by p).
`sigma.hat`	Estimate of the residual standard error.
`prediction`	Matrix of estimated additive components for the points listed in the argument point.
`mul`	A vector of size p showing in each component the estimated intercept that considers only that direction of interest when using the type `'alpha'` method.
`g.derivative`	Matrix of estimated derivatives of the additive components (only when qderivate is `TRUE`) (n by p).
`prediction.derivate`	Matrix of estimated derivatives of the additive components for the points listed in the argument point (only when qderivate is `TRUE`).
`Xp`	Matrix of explanatory variables.
`yp`	Vector of responses.
`formula`	Model formula

Author(s)

Alejandra Martinez, ale_m_martinez@hotmail.com, Matias Salibian-Barrera

References

Boente G. and Martinez A. (2017). Marginal integration M-estimators for additive models. TEST, 26(2), 231-260. https://doi.org/10.1007/s11749-016-0508-0

Examples

function.g1 <- function(x1) 24*(x1-1/2)^2-2
function.g2 <- function(x2) 2*pi*sin(pi*x2)-4
set.seed(140)
n <- 150
x1 <- runif(n)
x2 <- runif(n)
X <- cbind(x1, x2)
eps <- rnorm(n,0,sd=0.15)
regresion <- function.g1(x1) + function.g2(x2)
y <- regresion + eps
bandw <- matrix(0.25,2,2)
set.seed(8090)
nQ <- 80 
Qmeasure <- matrix(runif(nQ*2), nQ, 2)
fit.rob <- margint.rob(y ~ X, windows=bandw, type='alpha', degree=1, Qmeasure=Qmeasure)