Local likelihood bandwidth and/or family selection.

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

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
)

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.

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.

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)
})
#>    user  system elapsed 
#>   1.784   0.019   1.803 

# 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)