Estimate parameters of stable laws

Estimates the four parameters of stable distributions using one of the methods implemented in StableEstim. This is the main user-level function but the individul methods are available also as separate functions.

Estim(EstimMethod = c("ML", "GMM", "Cgmm","Kout"), data, theta0 = NULL,
      ComputeCov = FALSE, HandleError = TRUE, ...)

Arguments

EstimMethod

Estimation method to be used, one of "ML" (maximum likelihood, default), "GMM" (generalised method of moment with finite moment conditions), "Cgmm" (GMM with continuum moment conditions), and "Kout" (Koutrouvelis regression method).

data

Data used to perform the estimation, a numeric vector.

theta0

Initial values for the 4 parameters. If NULL (default), initial values are computed using the fast Kogon-McCulloch method, see IGParametersEstim; vector of length 4.

ComputeCov

Logical flag: if TRUE, the asymptotic covariance matrix (4x4) is computed (except for the Koutrouvelis method).

HandleError

Logical flag: if TRUE and if an error occurs during the estimation procedure, the computation will carry on and NA will be returned. Useful for Monte Carlo simulations, see Estim_Simulation.

...

Other arguments to be passed to the estimation function, such as the asymptotic confidence level, see Details.

Details

Estim is the main estimation function in package StableEstim.

This function should be used in priority for estimation purpose as it provides more information about the estimator. However, user needs to pass the appropriate parameters to the selected method in .... See the documentation of the selected method.

Asymptotic Confidence Intervals: The normal asymptotic confidence intervals (CI) are computed. The user can set the level of confidence by inputing the level argument (in the "\dots"); default level=0.95. The theoretical justification for asymptotic normal CI can be found in the references for the individual methods. Note the CI's are not computed for the Koutrouvelis regression method.

Value

an object of class Estim, see Estim-class for more details

See also

CgmmParametersEstim, GMMParametersEstim, MLParametersEstim, KoutParametersEstim for the individual estimation methods;

IGParametersEstim for fast computation of initial values.

Examples

## general inputs
theta <- c(1.45, 0.55, 1, 0)
pm <- 0
set.seed(2345)
x <- rstable(200, theta[1], theta[2], theta[3], theta[4], pm)

objKout <- Estim(EstimMethod = "Kout", data = x, pm = pm, 
                     ComputeCov = FALSE, HandleError = FALSE, 
                     spacing = "Kout")