Spline ML example
In circularEV: Extreme Value Analysis for Circular Data

knitr::opts_chunk$set(
  collapse = TRUE,
  comment = "#>",
        echo=TRUE, results='hold', warning=F, cache=F, eval=T,
  #dev = 'pdf', 
  message=F, 
  fig.width=5, fig.height=5, # fig.retina=0.7,
  tidy.opts=list(width.cutoff=75), tidy=TRUE
)
old <- options(scipen = 1, digits = 4)

library(circularEV)
require(plotly)

Reading Data

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)

PlotData(Data=Data, drc=drc, thr=NULL, pointSize=1, cex.axis=15, cex.lab=2, thrWidth=2)
PolarPlotData(Data=Data, drc=drc, thr=NULL, pointSize=4, fontSize=14,
              thrWidth=4, ylim=c(0,max(Data)) )

Threshold selection

Grid values at which the estimation is performed:

thetaVec <- 1:360

thrResultML <- ThrSelection(Data=Data, drc=drc, h=60, b=0.35, thetaGrid=thetaVec,
                         EVIestimator="ML", useKernel=T, concent=10, bw=30, numCores=2)$thr

data(thresholdExampleML)
thrResultML <- thresholdExampleML

PlotData(Data=Data, drc=drc, thr=thrResultML, pointSize=1, cex.axis=15, cex.lab=2, thrWidth=2)

PolarPlotData(Data=Data, drc=drc, thr=thrResultML, pointSize=4, fontSize=12, 
              thrWidth=4, ylim=c(0,max(Data)))

Estimation of spline ML model

The code below performs optimisation for a unique pair of lambda and kappa.

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)

High Quantiles

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)

# 10000-year level
PlotRL(RLBootList=RLBoot, thetaGrid=thetaVec, Data=Data, drc=drc,
       TTs=c(100, 10000), whichPlot=2, 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=2, alpha=0.05, ylim=c(0, 25),
            pointSize=4, fontSize=12, lineWidth=2)