heavyFit: Estimation of Location and Scatter using multivariate heavy-tailed distributions

Description

Estimates the center vector and scatter matrix assuming that the data came from a multivariate heavy-tailed distribution. This provides some degree of robustness to outliers without giving a high breakdown point.

Usage

heavyFit(x, data, family = Student(df = 4), subset, na.action, control)

Arguments

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 x 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 "heavyFit" 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 location vector.

Scatter

final estimate of the scale matrix.

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 estimates.

References

Kent, J.T., Tyler, D.E., and Vardi, Y. (1994). A curious likelihood identity for the multivariate t-distribution. Communications in Statistics - Simulation and Computation 23, 441-453.

Lange, K., Little, R.J.A., and Taylor, J.M.G. (1989). Robust statistical modeling using the t distribution. Journal of the American Statistical Association 84, 881-896.

Little, R.J.A. (1988). Robust estimation of the mean and covariance matrix from data with missing values. Applied Statistics 37, 23-38.

Examples

Run this code

# NOT RUN {
data(creatinine)
fit <- heavyFit(~ log(WT) + log(SC) + log(140 - Age) + log(CR), data = creatinine,
  family = Student(df = 4))
summary(fit)
# }