# mvt.ecme: Estimate Parameters of a Multivariate t Distribution Using... In miscF: Miscellaneous Functions

## Description

Use the Expectation/Conditional Maximization Either (ECME) algorithm to obtain estimate of parameters of a multivariate t distribution.

## Usage

 `1` ``` mvt.ecme(X, lower.v, upper.v, err=1e-4) ```

## Arguments

 `X` a matrix of observations with one subject per row. `lower.v` lower bound of degrees of freedom (df). `upper.v` upper bound of df. `err` the iteration stops when consecutive difference in percentage of df reaches this bound. The default value is 1e-4.

## Details

They are number of forms of the generalization of the univariate student-t distribution to multivariate cases. This function adopts the widely used representation as a scale mixture of normal distributions.

To obtain the estimate, the algorithm adopted is the Expectation/Conditional Maximization Either (ECME), which extends the Expectation/Conditional Maximization (ECM) algorithm by allowing CM-steps to maximize either the constrained expected complete-data log-likelihood, as with ECM, or the correspondingly constrained actual log-likelihood function.

## Value

 `Mu` estimate of location. `Sigma` estimate of scale matrix. `v` estimate of df.

## References

Chuanhai Liu (1994) Statistical Analysis Using the Multivariate t Distribution Ph. D. Dissertation, Harvard University

## Examples

 ``` 1 2 3 4 5 6 7 8 9 10 11 12 13 14``` ``` mu1 <- mu2 <- sigma12 <- sigma22 <- 100 rho12 <- 0.7 Sigma <- matrix(c(sigma12, rho12*sqrt(sigma12*sigma22), rho12*sqrt(sigma12*sigma22), sigma22), nrow=2) k <- 5 N <- 100 require(mvtnorm) X <- rmvt(N, sigma=Sigma, df=k, delta=c(mu1, mu2)) result <- mvt.ecme(X, 3, 300) result\$Mu result\$Sigma result\$v ```

miscF documentation built on April 14, 2020, 7:01 p.m.