MLEfit {FitDynMix}

Estimating a dynamic mixture via MLE

Description

This function fits a dynamic mixture via standard maximum likelihood. Currently only implemented for the lognormal - generalized Pareto case, with Cauchy or exponential weight.

Usage

MLEfit(yObs, bootreps, intTol = 1e-04, weight)

Arguments

yObs

numerical vector: observed sample.

bootreps

non-negative integer: number of bootstrap replications. If equal to 0, no standard errors are computed.

intTol

non-negative scalar: threshold for stopping the computation of the integral in the normalization constant: if the integral on the interval from n-1 to n is smaller than intTol, the approximation procedure stops.

weight

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

Details

Starting values for mu and sigma are the lognormal MLEs computed with the observations below the median. Initial values for xi and tau are the GPD MLEs obtained with the observations above the median. For the location and scale parameter of the Cauchy, we respectively use the first quartile and abs(log(sd(x)/2)). For the parameter of the exponential, we use abs(log(sd(x)/2)).

Value

MLEpars vector: maximum likelihood estimates and maximized log-likelihood.

MLEboot matrix: maximum likelihood estimates obtained in each bootstrap replication.

sdMLE vector: bootstrap standard deviation of the MLEs.

References

Bee M (2023). “Unsupervised mixture estimation via approximate maximum likelihood based on the Cramér - von Mises distance.” Computational Statistics & Data Analysis, 185, 107764.

See Also

AMLEfit

Examples

mixFit <- MLEfit(Metro2019,0,,'cau')