Parametric bootstrap confidence interval for the parameter theta for Liouville copula

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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

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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

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

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theta.bci(B=99, family="gumbel", alphavec=c(2,3), n=1000, 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))

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