# theta.bci: Parametric bootstrap confidence interval for the parameter... In lcopula: Liouville Copulas

 theta.bci R Documentation

## Parametric bootstrap confidence interval for the parameter theta for Liouville copula

### Description

The parametric bootstrap provides confidence intervals by repeatedly sampling datasets from the postulated Liouvilla copula model. If d=2 and the model is either gumbel or clayton, the value of Kendall's \tau is calculated from the sample, and the confidence interval or the quantiles correspond to the inverse \tau^{-1}(\tau(\theta)) for the bootstrap quantile values of \tau (using monotonicity).

### Usage

theta.bci(
B = 1999,
family,
alphavec,
n,
theta.hat,
quant = c(0.025, 0.975),
silent = FALSE
)


### Arguments

 B number of bootstrap replicates family family of the Liouville copula. Either "clayton", "gumbel", "frank", "AMH" or "joe" alphavec vector of Dirichlet allocations (must be a vector of integers) n sample size theta.hat estimate of theta quant if the vector of probability is specified, the function will return the corresponding bootstrap quantiles silent boolean for output progress. Default is FALSE, which means iterations are printed if d>2.

### Details

Install package wdm to speed up calculation of Kendall's tau.

Since no closed-form formulas exist for the other models or in higher dimension, the method is extremely slow since it relies on maximization of a new sample from the model and look up the corresponding parameters.

### Value

a list with a 95 and the bootstrap values of Kendall's tau in boot_tau if d=2 and the model is either gumbel or clayton. Otherwise, the list contains boot_theta.

### Examples

## Not run:
theta.bci(B=99, family="gumbel", alphavec=c(2,3), n=100, theta.hat=2)
theta.bci(B=19, family="AMH", alphavec=c(1,2), n=100, theta.hat=0.5, quant=c(0.05,0.95))
theta.bci(B=19, family="frank", alphavec=c(1,2,3), n=100, theta.hat=0.5, quant=c(0.05,0.95))

## End(Not run)


lcopula documentation built on April 21, 2023, 9:07 a.m.