# Spline ML fitting ```r 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 ```r 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") ```

SplineML function