SplineML {circularEV}

Spline ML fitting

Description

Spline ML fitting

Usage

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

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.

Value

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

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")