View source: R/SplineFitDepFct.R
SplineFitDepFct | R Documentation |
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.
SplineFitDepFct(x, y = NULL, alpha = 0.01, integ.value)
x , y |
vectors giving the coordinates of the points to be approximated. Alternatively a single plotting structure can be specified: see |
alpha |
real, the smoothing parameter for the smoothing splines. |
integ.value |
real, non-negative value that should be less than two; see ‘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.
A function, created by splinefun
, that evaluates the natural cubic spline that was fitted to the data.
Nader Tajvidi Nader.Tajvidi@matstat.lu.se
Berwin A Turlach Berwin.Turlach@gmail.com
Hall, P. and Tajvidi, N. (2000). Distribution and dependence-function estimation for bivariate extreme-value distributions. Bernoulli 6(5): 835–844. \Sexpr[results=rd]{tools:::Rd_expr_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. \Sexpr[results=rd]{tools:::Rd_expr_doi("10.1111/j.1467-842X.2004.00316.x")}.
NonparEstDepFct
, NewBEVSplineCopula
## 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")
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