estim_em_cm: Estimating curvature measures from bivariate chi-bar-squared...
In damelunx/symconivol: A package for curvature measures of symmetric cones

Description Usage Arguments Details Value See also Examples

estim_em_cm produces EM-type iterates from a two-column matrix whose rows form iid samples from a bivariate chi-bar-squared distribution.

1 2	estim_em_cm(d, low, upp, m_samp, N = 20, no_of_lcc_projections = 1, data = NULL)

`d`	the dimension of the bivariate chi-bar-squared distribution.
`low`	lower bound for `k`; has to be `>0`
`upp`	upper bound for `k`; has to be `<d`
`m_samp`	two-column matrix whose rows from iid samples from a bivariate chi-bar-squared distribution.
`N`	the number of iterates that shall be produced.
`no_of_lcc_projections`	number of projections on the log-concavity cone
`data`	output of `prepare_em_cm(d, low, upp, m_samp)`; this can be called outside and passed as input to avoid re-executing this potentially time-consuming step.

The sequence of iterates may or may not converge to the maximum likelihood estimate of the mixing weights of the distribution. Log-concavity of the weights is enforced by projecting the logarithms onto the cone of log-concave sequences; this can be turned off by setting no_of_lcc_projections=0. This function is adapted from estim_em from the conivol package, the difference being that the support of the weights is strictly between the boundary cases. It is simplified in that the initial estimate is always the uniform distribution, and the parity equation, which does not hold for curvature measures, will not be enforced.

The output of estim_em_cm is a list of an (N+1)-by-(upp-low+1) matrix whose rows constitute EM-type iterates, which may or may not converge to the maximum likelihood estimate of the mixing weights of the bivariate chi-bar-squared distribution, and the corresponding values of the log-likelihood function.

estim_em, constr_eigval, constr_eigval_to_bcbsq, prepare_em_cm, indnorm_to_unnorm

Package: symconivol

CM <- curv_meas_exact(4,3)$A[,2]
CM <- CM/sum(CM)

m_samp <- conivol::rbichibarsq(1e5,CM)

d   <- 15
low <- 1
upp <- 9
est <- estim_em_cm( d, low, upp, m_samp )

plot(1+low:upp, CM[1+low:upp])
lines(1+low:upp, CM[1+low:upp], col="red")
lines(1+low:upp, est[1,])
lines(1+low:upp, est[5,])
lines(1+low:upp, est[10,])
lines(1+low:upp, est[21,])