R: Covariance Estimation for Multivariate t Distribution

cov.trob {MASS} | R Documentation

## Covariance Estimation for Multivariate t Distribution

### 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

    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

    cov.trob(stackloss)

[Package MASS version 7.3-52 Index]