LocalCop (version 0.0.2)

CondiCopSelect: Local likelihood bandwidth and/or family selection.

Description

Selects among a set of bandwidths and/or copula families the one which maximizes the cross-validated local likelihood. See CondiCopLikCV() for details.

Usage

CondiCopSelect(
  u1,
  u2,
  family,
  x,
  xind = 100,
  degree = 1,
  nu,
  kernel = KernEpa,
  band,
  nband = 6,
  optim_fun,
  cv_all = FALSE,
  full_out = TRUE,
  cl = NA
)

Value

If full_out = FALSE, a list with elements family and bandwidth containing the selected value of each. Otherwise, a list with the following elements:

cv

A data frame with nBF = length(band) x length(family) rows and columns named family, band, and cv containing the cross-validated likelihood evaluated at each combination of bandwidth and family values.

x

The sorted values of x.

eta

A length(x) x nBF matrix of eta estimates, the columns of which are in the same order as the rows of cv.

nu

A vector of length nBF second copula parameters, with zero if they don't exist.

Arguments

u1

Vector of first uniform response.

u2

Vector of second uniform response.

family

Vector of integers specifying the family set. See ConvertPar().

x

Vector of observed covariate values.

xind

Specification of xind for each bandwidth. Can be a scalar integer, a vector of nband integers, or a list of nband vectors of integers.

degree

Integer specifying the polynomial order of the local likelihood function. Currently only 0 and 1 are supported.

nu

Optional vector of fixed nu parameter for each family. If missing or NA get estimated from the data (if required)

kernel, optim_fun, cl

See CondiCopLocFit().

band

Vector of positive numbers specifying the bandwidth value set.

nband

If band is missing, automatically choose nband bandwidth values spanning the range of x.

cv_all

If FALSE, evaluate the CV likelihood at only the leave-one-out observations specified by xind. Otherwise, interpolate the leave-one-out estimates of eta to all values in x, and evaluate the CV likelihood at all observations.

full_out

Logical; whether or not to output all fitted models or just the selected family/bandwidth combination. See Value.

Examples

# simulate data
set.seed(123)
family <- 5 # Frank copula
n <- 1000
x <- runif(n) # covariate values
eta_fun <- function(x) 2*cos(12*pi*x) # copula dependence parameter
eta_true <- eta_fun(x)
par_true <- BiCopEta2Par(family, eta = eta_true)
udata <- VineCopula::BiCopSim(n, family=family,
                              par = par_true$par)

# bandwidth and family selection
bandset <- c(.01, .04, .1) # bandwidth set
famset <- c(2, 5) # family set
n_loo <- 100 # number of leave-one-out observations in CV likelihood calculation
system.time({
  cvsel <- CondiCopSelect(u1= udata[,1], u2 = udata[,2],
                          x = x, family = famset, band = bandset,
                          xind = n_loo)
})

# compare estimates to true value
xseq <- cvsel$x
famsel <- cvsel$cv$family
bandsel <- cvsel$cv$band
etasel <- cvsel$eta
clrs <- c("red", "blue", "green4")
names(clrs) <- bandset

plot_fun <- function(fam) {
  nband <- length(bandset)
  if(fam == 2) {
    famind <- 1:nband
    main <- "Student-t Copula"
  } else {
    famind <- nband+1:nband
    main <- "Frank Copula"
  }
  plot(xseq, BiCopEta2Tau(family, eta = eta_fun(xseq)),
       type = "l", lwd = 2, ylim = c(-.5, .5),
       xlab = expression(x), ylab = expression(tau(x)),
       main = main)
  for(ii in famind) {
    lines(xseq, BiCopEta2Tau(fam, eta = etasel[,ii]),
          col = clrs[as.character(bandsel[ii])], lwd = 1)
  }
  legend("bottomright", fill = clrs,
         legend = paste0("band_", bandsel[famind],
                         " = ", signif(cvsel$cv$cv[famind], 3)))
}

oldpar <- par(mfrow = c(1,2))
plot_fun(2)
plot_fun(5)
par(oldpar)