fit_mvss {mvpd}

Fit a Multivariate Subgaussian Distribution

Description

Estimates the parameters (namely, alpha, shape matrix Q, and location vector) of the multivariate subgaussian distribution for an input matrix X.

Usage

fit_mvss(x)

Arguments

x

a matrix for which the parameters for a d-dimensional multivariate subgaussian distribution will be estimated. The number of columns will be d.

Details

Using the protocols outlined in Nolan (2013), this function uses libstable4u's univariate fit functions for each component.

Value

A list with parameters from the column-wise univariate fits and the multivariate alpha and shape matrix estimates (the univ_deltas are the mult_deltas):

• univ_alphas - the alphas from the column-wise univariate fits

• univ_betas - the betas from the column-wise univariate fits

• univ_gammas - the gammas from the column-wise univariate fits

• univ_deltas - the deltas from the column-wise univariate fits

• mult_alpha - the mean(univ_alphas); equivalently the multivariate alpha estimate

• mult_Q_raw - the multivariate shape matrix estimate (before applying nearPD())

• mult_Q_posdef - the nearest positive definite multivariate shape matrix estimate, nearPD(mult_Q_raw)

References

Nolan JP (2013), Multivariate elliptically contoured stable distributions: theory and estimation. Comput Stat (2013) 28:2067–2089 DOI 10.1007/s00180-013-0396-7

See Also

Rfast::mvnorm.mle, alphastable::mfitstab.elliptical

Examples

## create a 4x4 shape matrix symMat
S <- matrix(rnorm(4*4, mean=2, sd=4),4); 
symMat <- as.matrix(Matrix::nearPD(0.5 * (S + t(S)))$mat)
symMat
## generate 10,000 r.v.'s from 4-dimensional mvss
X <- mvpd::rmvss(1e4, alpha=1.5, Q=symMat, delta=c(1,2,3,4))
## use fit_mvss to recover the parameters, compare to symMat
fmv <- mvpd::fit_mvss(X)
fmv
symMat
## then use the fitted parameters to calculate a probability:
mvpd::pmvss(lower=rep(0,4),
            upper=rep(5,4),
            alpha=fmv$mult_alpha,
            Q=fmv$mult_Q_posdef,
            delta=fmv$univ_deltas,
            maxpts.pmvnorm = 25000*10)