# 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 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 26, 2022, 1:08 a.m.