exceedance.ci {ExceedanceTools}

Return confidence region

Description

exceedance.ci returns a confidence set for an exceedance region or contour line.

Usage

exceedance.ci(statistic.sim.obj, conf.level = 0.95, type = "null")

Arguments

statistic.sim.obj

An object returned from the statistic.sim function.

conf.level

The desired confidence level of the confidence region.

type

Whether the function should return the null region or rejection region of exceedance confidence region Options are "null" or "rejection". Default is "null".

Value

Returns a numeric vector with the set of pixels comprising the null or rejection region related to statistic.sim.obj.

Author(s)

Joshua French

Examples

library(SpatialTools)

# Example for exceedance regions

set.seed(10)
# Load data
data(sdata)
# Create prediction grid
pgrid <- create.pgrid(0, 1, 0, 1, nx = 26, ny = 26)
pcoords <- pgrid$pgrid
# Create design matrices
coords = cbind(sdata$x1, sdata$x2)
X <- cbind(1, coords)
Xp <- cbind(1, pcoords)

# Generate covariance matrices V, Vp, Vop using appropriate parameters for 
# observed data and responses to be predicted
spcov <- cov.sp(coords = coords, sp.type = "exponential", 
 sp.par = c(1, 1.5), error.var = 1/3, finescale.var = 0, pcoords = pcoords)

# Predict responses at pgrid locations
krige.obj <- krige.uk(y = as.vector(sdata$y), V = spcov$V, Vp = spcov$Vp, 
 Vop = spcov$Vop, X = X, Xp = Xp, nsim = 100, 
 Ve.diag = rep(1/3, length(sdata$y)) , method = "chol")
                
# Simulate distribution of test statistic for different alternatives
statistic.sim.obj.less <- statistic.sim(krige.obj = krige.obj, level = 5, 
 alternative = "less")
statistic.sim.obj.greater <- statistic.sim(krige.obj = krige.obj, level = 5,
 alternative = "greater")
# Construct null and rejection sets for two scenarios
n90 <- exceedance.ci(statistic.sim.obj.less, conf.level = .90, type = "null")
r90 <- exceedance.ci(statistic.sim.obj.greater,conf.level = .90, type = "rejection")       
# Plot results
plot(pgrid, n90, col="blue", add = FALSE, xlab = "x", ylab = "y")
plot(pgrid, r90, col="orange", add = TRUE)
legend("bottomleft", 
 legend = c("contains true exceedance region with 90 percent confidence", 
   "is contained in true exceedance region with 90 percent confidence"),
   col = c("blue", "orange"), lwd = 10)