Covariance Estimation for Multivariate t Distribution

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.

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. (2002) Modern Applied Statistics with S-PLUS. Fourth Edition. Springer.

See also

cov, cov.wt, cov.mve

Examples

cov.trob(stackloss)
#> $cov
#>            Air.Flow Water.Temp Acid.Conc. stack.loss
#> Air.Flow   60.47035  17.027203  18.554452   62.28032
#> Water.Temp 17.02720   8.085857   5.604132   20.50469
#> Acid.Conc. 18.55445   5.604132  24.404633   16.91085
#> stack.loss 62.28032  20.504687  16.910855   72.80743
#> 
#> $center
#>   Air.Flow Water.Temp Acid.Conc. stack.loss 
#>   58.96905   20.79263   86.05588   16.09028 
#> 
#> $n.obs
#> [1] 21
#> 
#> $call
#> cov.trob(x = stackloss)
#> 
#> $iter
#> [1] 5
#>