SplineML function

Spline ML fitting

SplineML(
  excesses,
  drc,
  thetaVec = 0:360,
  nBoot = 100,
  numIntKnots = 10,
  knotsType = "eqSpaced",
  lambda = seq(0, 2, by = 0.5),
  kappa = seq(0, 2, by = 0.5),
  nCandidatesInit = 1000,
  numCores = 2
)

Arguments

• excesses: Excesses data
• drc: Directional covariate
• thetaVec: Grid values at which the threshold will be evaluated
• nBoot: Number of bootstrap resamples
• numIntKnots: Number of internal knots
• knotsType: Position of knots. Default to "eqSpaced". Otherwise, the knots will be placed at the quantiles of observed directions.
• lambda: Penalty parameter values for lambda
• kappa: Penalty parameter values for kappa
• nCandidatesInit: Number of initial parameter vectors. Optimisation will start with the best.
• numCores: Number of CPU cores to be used

Returns

List of bootstrap estimates of shape and scale, and optimal values of lambda and kappa.

Details

See Konzen, E., Neves, C., and Jonathan, P. (2021). Modeling nonstationary extremes of storm severity: Comparing parametric and semiparametric inference. Environmetrics, 32(4), e2667.

Examples

data(HsSP)
data(drc)
timeRange <- 54.5

idx <- order(drc)
drc <- drc[idx]
Data <- HsSP[idx]
set.seed(1234)
Data <- Data + runif(length(Data), -1e-4, 1e-4)

thetaVec <- 1:360

data(thresholdExampleML) # loads threshold example
thrResultML <- thresholdExampleML

lambda <- 100
kappa <- 40

thrPerObs <- thrResultML[drc]
excess <- Data - thrPerObs
drcExcess <- drc[excess>0]
excess <- excess[excess>0]


splineFit <- SplineML(excesses = excess, drc = drcExcess, nBoot = 30,
                      numIntKnots = 16, lambda=lambda, kappa=kappa, numCores=2)

xiBoot <- splineFit$xi
sigBoot <- splineFit$sig

PlotParamEstim(bootEstimates=xiBoot, thetaGrid=0:360, ylab=bquote(hat(xi)),
               alpha=0.05, ylim=NULL, cex.axis=15, cex.lab=2, thrWidth=2)

PlotParamEstim(bootEstimates=sigBoot, thetaGrid=0:360, ylab=bquote(hat(sigma)),
               alpha=0.05, ylim=NULL, cex.axis=15, cex.lab=2, thrWidth=2)

h <- 60 # needed for calculating local probability of exceedances
RLBoot <- CalcRLsplineML(Data=Data, drc=drc, xiBoot=xiBoot, sigBoot=sigBoot, h=h,
                         TTs=c(100, 10000), thetaGrid=thetaVec,
                         timeRange=timeRange, thr=thrResultML)

# 100-year level
PlotRL(RLBootList=RLBoot, thetaGrid=thetaVec, Data=Data, drc=drc,
       TTs=c(100, 10000), whichPlot=1, alpha=0.05, ylim=NULL,
       pointSize=1, cex.axis=15, cex.lab=2, thrWidth=2)

PolarPlotRL(RLBootList=RLBoot, thetaGrid=thetaVec, Data=Data, drc=drc,
            TTs=c(100, 10000), whichPlot=1, alpha=0.05, ylim=c(0, 25),
            pointSize=4, fontSize=12, lineWidth=2)


## See also examples in vignette:
# vignette("splineML", package = "circularEV")