studentFit {MVT}

Estimation of mean and covariance using the multivariate t-distribution

Description

Estimates the mean vector and covariance matrix assuming the data came from a multivariate t-distribution: this provides some degree of robustness to outlier without giving a high breakdown point.

Usage

studentFit(x, data, family = Student(eta = .25), covStruct = "UN", subset, na.action, 
control)

Arguments

x

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 multivariate t-distribution with 0.25 as shape parameter is considered (using eta = 0 allows to tackle the multivariate normal distribution).

covStruct

a character string specifying the type of covariance structure. The options available are: "UN" (unstructured) general covariance matrix with no additional structure (default), "CS" (compound symmetry) corresponding to a constant correlation or equicorrelation, "DIAG" (diagonal) representing a diagonal positive-definite matrix, "HOMO" (homogeneous) meaning a covariance matrix with homogeneous variances.

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 MVT.control.

Value

A list with class 'studentFit' containing the following components:

call

a list containing an image of the studentFit call that produced the object.

family

the Student 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.

eta

final estimate of the shape parameter, if requested.

Generic function print show the results of the fit.

References

Kent, J.T., Tyler, D.E., 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., Taylor, J.M.G. (1989). Robust statistical modeling using the t distribution. Journal of the American Statistical Association 84, 881-896.

Osorio, F., Galea, M., Henriquez, C., Arellano-Valle, R. (2023). Addressing non-normality in multivariate analysis using the t-distribution. AStA Advances in Statistical Analysis. doi: 10.1007/s10182-022-00468-2

See Also

cov, cov.rob, cov.trob

Examples

data(PSG)
fit <- studentFit(~ manual + automated, data = PSG, family = Student(eta = 0.25))
fit