heavyGrubbs: Estimation for the Grubbs' model under heavy-tailed...

In heavy: Robust Estimation Using Heavy-Tailed Distributions

Description

This function fits a Grubbs' model (using the parameterization of Theobald and Mallison, 1978) considering heavy-tailed distributions. This provides some degree of robustness to outliers.

Usage

heavyGrubbs(y, data, family = Student(df = 4), subset, na.action, control)

Arguments

y	a formula or a numeric matrix or an object that can be coerced to a numeric matrix.
data	an optional data frame (or similar: see model.frame), used only if y is a formula. By default the variables are taken from environment(formula).
family	a description of the error distribution to be used in the model. By default the Student-t distribution with 4 degrees of freedom is considered.
subset	an optional expression indicating the subset of the rows of data that should be used in the fitting process.
na.action	a function that indicates what should happen when the data contain NAs.
control	a list of control values for the estimation algorithm to replace the default values returned by the function heavy.control.

Value

A list with class "heavyGrubbs" containing the following components:

call	a list containing an image of the heavyFit call that produced the object.
family	the heavy.family object used, with the estimated shape parameters (if requested).
center	final estimate of the center parameters (related with the additive biases).
phi	final estimate of the dispersion parameters.
z	estimated latent variables.
logLik	the log-likelihood at convergence.
numIter	the number of iterations used in the iterative algorithm.
weights	estimated weights corresponding to the assumed heavy-tailed distribution.
distances	estimated squared Mahalanobis distances.
acov	asymptotic covariance matrix of the center estimate.

References

Osorio, F., Paula, G.A., Galea, M. (2009). On estimation and influence diagnostics for the Grubbs' model under heavy-tailed distributions. Computational Statistics and Data Analysis 53, 1249-1263.

Examples

data(thermocouples)
fit <- heavyGrubbs(100 * thermocouples, family = Student(df = 4))
fit

heavy documentation built on Oct. 30, 2019, 9:48 a.m.