CENoisyFitBoot {FitDynMix}

Cross-Entropy estimation and bootstrap standard errors

Description

This function estimates a dynamic mixture by means of the noisy Cross-Entropy method and computes bootstrap standard errors. Currently only implemented for the lognormal - generalized Pareto, with Cauchy or exponential weight. Bootstrap standard errors are computed in parallel.

Usage

CENoisyFitBoot(
  yObs,
  nboot,
  rho,
  maxiter,
  alpha,
  nsim,
  nrepsInt,
  xiInst,
  betaInst,
  eps,
  r = 5,
  weight
)

Arguments

yObs

numerical vector: observed random sample from the mixture.

nboot

integer: number of bootstrap replications for computing the standard errors. If nboot = 0, no standard errors are computed.

rho

real in (0,1): parameter determining the quantile of the log-likelihood values to be used at each iteration.

maxiter

non-negative integer: maximum number of iterations.

alpha

real in (0,1): smoothing parameter.

nsim

non-negative integer: number of replications used in the normal and lognormal updating.

nrepsInt

non-negative integer: number of replications used in the Monte Carlo estimate of the normalizing constant.

xiInst

non-negative real: shape parameter of the instrumental GPD.

betaInst

non-negative real: scale parameter of the instrumental GPD.

eps

non-negative real: tolerance for the stopping criterion of the noisy Cross-Entropy method.

r

positive integer: length of window to be used in the stopping criterion.

weight

'cau' or 'exp': name of weight distribution.

Value

If nboot > 0, a list with the following elements:

estPars: Cross-Entropy estimates.

nit: number of iterations needed for convergence.

loglik: maximized log-likelihood.

bootPars: parameter estimates obtained for each bootstrap sample.

stddev: bootstrap standard errors.

If nboot = 0, only estPars, nit and loglik are returned.

Examples

res = CENoisyFitBoot(Metro2019,0,.05,20,.5,500,500,3,3,.01,5,'exp')