SplineFitDepFct {SimCop}

Fit a dependence function by spline smoothing

Description

Given estimates for the dependence function of a bivariate extreme value copula at specified points, this function fits a natural cubic smoothing spline, that is constrained to fulfill all the conditions of a dependence function, to the given estimates via quadratic programming.

Usage

SplineFitDepFct(x, y = NULL, alpha = 0.01, integ.value)

Arguments

x, y

vectors giving the coordinates of the points to be approximated. Alternatively a single plotting structure can be specified: see xy.coords.

alpha

real, the smoothing parameter for the smoothing splines.

integ.value

real, non-negative value that should be less than two; see ‘Details’

Details

integ.value should be between 0 and 2. If a value is specified, then an additional constraint is added to the quadratic program to ensure that the integeral (over 0 to 1) of the second derivative of the spline is larger or equal to integ.value. Choosing values close to 2 may lead to quadratic programms on which solve.QP reports inconsistent constraints.

Value

A function, created by splinefun, that evaluates the natural cubic spline that was fitted to the data.

Author(s)

Nader Tajvidi <[e-mail]>

Berwin A Turlach <[e-mail]>

References

Hall, P. and Tajvidi, N. (2000). Distribution and dependence-function estimation for bivariate extreme-value distributions. Bernoulli 6(5), 835–844. Doi:10.2307/3318758.

Hall, P. and Tajvidi, N. (2004). Prediction regions for bivariate extreme events. Australian & New Zealand Journal of Statistics 46(1), 99–112. Doi:10.1111/j.1467-842X.2004.00316.x.

See Also

NonparEstDepFct, NewBEVSplineCopula

Examples

## Data from Hall and Tajvidi (2004, ANZJS)
EstDF2 <- NonparEstDepFct(MaxTemp, convex = FALSE)

## Plot modified Pickands Function and area in which
## dependence function must lie
plot(EstDF2, ylim = c(0.5,1), xlab = "w", ylab = "A(w)", type="l", lty="longdash")
polygon(c(0, 0.5, 1, 0), c(1, 0.5, 1, 1))

## Fit spline to Pickands function and add to plot
splfit <- SplineFitDepFct(EstDF2)
curve(splfit, n = 301, add = TRUE, lty = "dashed")