MultiMapParameters: Mapping function for univariate distributions

In GAS: Generalized Autoregressive Score Models

Mapping function for univariate distributions

Description

Map unrestricted vector of parameters into the proper space. This function transforms the parameters updated using the GAS recursion into their proper space.

Usage

MultiMapParameters(Theta_tilde, Dist, N)

Arguments

Theta_tilde	numeric Vector of reparametrised parameters, see Details.
Dist	character Label of the conditional distribution, see DistInfo.
N	numeric Cross sectional dimension. Note that only iN<5 is supported.

Details

The order of the parameters is generally: locations, scales, correlations, shape. When the distribution defined by Dist does not have, say, the shape parameter, this should be simply omitted. See also DistInfo for specific distributions.

Value

A numeric vector of parameters.

Author(s)

Leopoldo Catania

Examples

# Map unrestricted parameters for the Multivariate Student-t distribution with N=3
library("GAS")

N = 3

Dist = "mvt"

# Vector of location parameters (this is not transformed).
Mu_tilde  = c(0.1,0.2,0.3)

# Vector of unrestricted scales parameters such that
# the scales will be equal to 1.0, 1.2 and 0.3, for the first, second and
# third variables, respectively.
Phi_tilde = c(log(1.0), log(1.2), log(0.3))

# The vector c(0.1,0.2,0.3) represents vec(R),
# where R is the correlation matrix.
# Note that is up to the user to ensure that
# vec(R) implies a proper correlation matrix
# The function UnMapR_C transforms vec(R) in a vector of unrestricted parameters. It is
# the inverse of the hyperspherical coordinates transformration.

Rho_tilde = UnMapR_C(c(0.1,0.2,0.3), N)

# Vector of unconditional reparametrised parameters such that the
# degrees of freedom are 7.
#
# LowerNu() prints the lower bound numerical parameter for the degree
# of freedom, see help(LowerNu)
#

Theta_tilde = c(Mu_tilde, Phi_tilde , Rho_tilde, log(7 - LowerNu()))

Theta = MultiMapParameters(Theta_tilde, Dist, N)

Theta

GAS documentation built on Sept. 11, 2024, 8:13 p.m.