CENoisyFit {FitDynMix}

Cross-Entropy estimation

Description

This function estimates a dynamic mixture by means of the noisy Cross-Entropy method. Currently only implemented for the lognormal - generalized Pareto case, with Cauchy or exponential weight. This is mainly an auxiliary function, not suitable for the final user. Use CeNoisyFitBoot instead.

Usage

CENoisyFit(
  x,
  rawdata,
  rho,
  maxiter,
  alpha,
  nsim,
  nrepsInt,
  xiInst,
  betaInst,
  eps,
  r = 5,
  weight
)

Arguments

x

list: sequence of integers 1,...,K, where K is the mumber of datasets. Set x = 1 in case of a single dataset.

rawdata

either a list of vectors or a vector: in the former case, each vector contains a dataset to be used for estimation.

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.

Details

See Rubinstein and Kroese (2004, chap. 6).

Value

For each dataset, a list with the following elements is returned:

V (nreps x 12) matrix: updated mean and variance of the distributions used in the stochastic program. nit (positive integer): number of iterations needed for convergence. loglik (scalar): maximized log-likelihood.

References

Rubinstein RY, Kroese DP (2004). The Cross-Entropy Method. Springer.

See Also

CENoisyFitBoot

Examples

maxiter = 10
alpha = .5
rho = .05
eps = 1e-2
nsim = 1000
nrepsInt = 1000
xiInst = 3
betaInst = 3
r = 5
res <- CENoisyFit(1,Metro2019,rho,maxiter,alpha,nsim,nrepsInt,xiInst,betaInst,eps,r,'exp')