# cov.trob: Covariance Estimation for Multivariate t Distribution In MASS: Support Functions and Datasets for Venables and Ripley's MASS

## 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

 ```1 2``` ```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

 `1` ```cov.trob(stackloss) ```

### Example output

```\$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
 21

\$call
cov.trob(x = stackloss)

\$iter
 5
```

MASS documentation built on May 3, 2021, 5:08 p.m.