Covariance Estimation for Multivariate t Distribution

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Description

Estimates a covariance or correlation 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

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cov.trob(x, wt = rep(1, n), cor = FALSE, center = TRUE, nu = 5,
         maxit = 25, tol = 0.01)

Arguments

x

data matrix. Missing values (NAs) are not allowed.

wt

A vector of weights for each case: these are treated as if the case i actually occurred wt[i] times.

cor

Flag to choose between returning the correlation (cor = TRUE) or covariance (cor = FALSE) matrix.

center

a logical value or a numeric vector providing the location about which the covariance is to be taken. If center = FALSE, no centering is done; if center = TRUE the MLE of the location vector is used.

nu

‘degrees of freedom’ for the multivariate t distribution. Must exceed 2 (so that the covariance matrix is finite).

maxit

Maximum number of iterations in fitting.

tol

Convergence tolerance for fitting.

Value

A list with the following components

cov

the fitted covariance matrix.

center

the estimated or specified location vector.

wt

the specified weights: only returned if the wt argument was given.

n.obs

the number of cases used in the fitting.

cor

the fitted correlation matrix: only returned if cor = TRUE.

call

The matched call.

iter

The number of iterations used.

References

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

Venables, W. N. and Ripley, B. D. (1999) Modern Applied Statistics with S-PLUS. Third Edition. Springer.

See Also

cov, cov.wt, cov.mve

Examples

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