Description Usage Arguments Value References See Also Examples

For the matrix variate normal distribution, maximum likelihood estimates
exist for *N > max(p/q,q/p)+1* and are unique for *N > max(p,q)*.
The number necessary for the matrix variate t has not been worked out but
this is a lower bound. This implements an ECME algorithm to estimate the
mean, covariance, and degrees of freedom parameters. An AR(1), compound
symmetry, or independence restriction can be proposed for either or both
variance matrices. However, if they are inappropriate for the data, they may
fail with a warning.

1 2 3 4 5 6 7 8 9 10 11 12 13 14 |

`data` |
Either a list of matrices or a 3-D array with matrices in dimensions 1 and 2, indexed by dimension 3. |

`row.mean` |
By default, |

`col.mean` |
By default, |

`row.variance` |
Imposes a variance structure on the rows. Either
'none', 'AR(1)', 'CS' for 'compound symmetry', 'Correlation' for a
correlation matrix, or 'Independence' for
independent and identical variance across the rows.
Only positive correlations are allowed for AR(1) and CS and these
restrictions may not be guaranteed to converge.
Note that while maximum likelihood estimators are available (and used)
for the unconstrained variance matrices, |

`col.variance` |
Imposes a variance structure on the columns. Either 'none', 'AR(1)', 'CS', 'Correlation', or 'Independence'. Only positive correlations are allowed for AR(1) and CS. |

`df` |
Starting value for the degrees of freedom. If |

`fixed` |
Whether |

`tol` |
Convergence criterion. Measured against square deviation between iterations of the two variance-covariance matrices. |

`max.iter` |
Maximum possible iterations of the algorithm. |

`U` |
(optional) Can provide a starting point for the U matrix. By default, an identity matrix. |

`V` |
(optional) Can provide a starting point for the V matrix. By default, an identity matrix. |

`...` |
(optional) additional arguments can be passed to |

Returns a list with the following elements:

`mean`

the mean matrix

`U`

the between-row covariance matrix

`V`

the between-column covariance matrix

`var`

the scalar variance parameter (the first entry of the covariances are restricted to unity)

`nu`

the degrees of freedom parameter

`iter`

the number of iterations

`tol`

the squared difference between iterations of the variance matrices at the time of stopping

`logLik`

log likelihood of result.

`convergence`

a convergence flag,

`TRUE`

if converged.`call`

The (matched) function call.

1 2 3 4 5 6 7 8 9 10 11 12 13 | ```
Thompson, G Z. R Maitra, W Q Meeker, A Bastawros (2019),
"Classification with the matrix-variate-t distribution", arXiv
e-prints arXiv:1907.09565 <https://arxiv.org/abs/1907.09565>
Dickey, James M. 1967. “Matricvariate Generalizations of the
Multivariate t Distribution and the Inverted Multivariate t
Distribution.” Ann. Math. Statist. 38 (2): 511–18.
\doi{10.1214/aoms/1177698967}
Liu, Chuanhai, and Donald B. Rubin. 1994. “The ECME Algorithm:
A Simple Extension of EM and ECM with Faster Monotone Convergence.”
Biometrika 81 (4): 633–48.
\doi{10.2307/2337067}
``` |

Meng, Xiao-Li, and Donald B. Rubin. 1993. “Maximum Likelihood Estimation via the ECM Algorithm: A General Framework.” Biometrika 80 (2): 267–78. doi: 10.1093/biomet/80.2.267

1 2 | ```
Rubin, D.B. 1983. “Encyclopedia of Statistical Sciences.” In, 4th ed.,
272–5. John Wiley.
``` |

`rmatrixnorm()`

, `rmatrixt()`

,
`MLmatrixnorm()`

1 2 3 4 5 6 7 8 9 | ```
set.seed(20180202)
# drawing from a distribution with specified mean and covariance
A <- rmatrixt(
n = 100, mean = matrix(c(100, 0, -100, 0, 25, -1000), nrow = 2),
L = matrix(c(2, 1, 0, .1), nrow = 2), list = TRUE, df = 5
)
# fitting maximum likelihood estimates
results <- MLmatrixt(A, tol = 1e-5, df = 5)
print(results)
``` |

Embedding an R snippet on your website

Add the following code to your website.

For more information on customizing the embed code, read Embedding Snippets.