fit_mvss() R function from [mvpd]

Fit a Multivariate Subgaussian Distribution

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


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.

Returns

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)

Details

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

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)

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

fit_mvss function