estparmtd function

Estimation of the Parameters of a Multivariate $t$ Distribution

Estimation of the degrees of freedom, mean vector and correlation matrix of a multivariate $t$ distribution (MTD).

estparmtd(x, eps = 1e-6, display = FALSE, plot = display)

Arguments

• x: numeric matrix or data frame.
• eps: numeric. Precision for the estimation of the parameters.
• display: logical. When TRUE the value of the nu parameter at each iteration is printed.
• plot: logical. When TRUE the successive values of the nu parameter are plotted, allowing to visualise its convergence.

Returns

A list of 3 elements:

• nu non-negative numeric value. The degrees of freedom.
• mu the mean vector.
• Sigma: symmetric positive-definite matrix. The correlation matrix.

with two attributes attr(, "epsilon") (precision of the result) and attr(, "k") (number of iterations).

Details

The EM method is used to estimate the parameters.

Examples

nu <- 3
mu <- c(0, 1, 4)
Sigma <- matrix(c(1, 0.6, 0.2, 0.6, 1, 0.3, 0.2, 0.3, 1), nrow = 3)
x <- rmtd(100, nu, mu, Sigma)

# Estimation of the parameters
estparmggd(x)

References

Doğru, F., Bulut, Y. M. and Arslan, O. (2018). Doubly reweighted estimators for the parameters of the multivariate t-distribution. Communications in Statistics - Theory and Methods. 47. tools:::Rd_expr_doi("10.1080/03610926.2018.1445861") .

See Also

dmtd: probability density of a MTD

rmtd: random generation from a MTD.

Author(s)

Pierre Santagostini, Nizar Bouhlel