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.
studentFit(x, data, family = Student(eta = .25), covStruct = "UN", subset, na.action,
control)A list with class 'studentFit' containing the following components:
a list containing an image of the studentFit call that produced the object.
the Student object used, with the estimated shape parameters (if requested).
final estimate of the location vector.
final estimate of the scale matrix.
the log-likelihood at convergence.
the number of iterations used in the iterative algorithm.
estimated weights corresponding to the assumed heavy-tailed distribution.
estimated squared Mahalanobis distances.
final estimate of the shape parameter, if requested.
Generic function print show the results of the fit.
a formula or a numeric matrix or an object that can be coerced to a numeric matrix.
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).
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).
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.
an optional expression indicating the subset of the rows of data that should be used in the fitting process.
a function that indicates what should happen when the data contain NAs.
a list of control values for the estimation algorithm to replace
the default values returned by the function MVT.control.
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. tools:::Rd_expr_doi("10.1007/s10182-022-00468-2")
cov, cov.rob, cov.trob
data(PSG)
fit <- studentFit(~ manual + automated, data = PSG, family = Student(eta = 0.25))
fit
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