Pointwise confidence intervals by bootstrap
Pointwise quantiles and survival probabilities confidence intervals using bootstrap.
bootCI.ts(X, t, Tgrid, h, kernel = TruncGauss.kernel, kpar = NULL, prob = 0.99, threshold = quantile(X, 0.99), B = 100, alpha = 0.05, type = "quantile", CritVal = 3.6, initprop = 1/10, gridlen = 100, r1 = 1/4, r2 = 1/20, plot = F)
X |
a vector of the observed values. |
t |
a vector of time covariates which should have the same length as X. |
Tgrid |
a sequence of times used to perform the cross validation (can be any sequence in the interval |
h |
a bandwidth value (vector values are not admitted). |
kernel |
a kernel function used to compute the weights in the time domain, with default the truncated gaussian kernel. |
kpar |
a value for the kernel function parameter, with no default value. |
prob |
used if type = "quantile", a scalar value in [0,1] which determines the quantile order (vector values are not admitted). |
threshold |
used if type = "survival", a scalar value in the domain of X. |
B |
an integer giving the number of bootstrap iterations. |
alpha |
the type 1 error of the bootstrap (1-alpha)-confidence interval. |
type |
type is either "quantile" or "survival". |
CritVal |
a critical value associated to the kernel function given by |
gridlen, initprop, r1, r2 |
parameters used in the function hill.adapt (see |
plot |
If |
For each point in Tgrid, generate B samples of X with replacement to estimate the quantile of order prob or the survival probability beyond threshold. Determine the bootstrap pointwise (1-alpha)-confidence interval for the quantiles or the survival probabilities.
The kernel implemented in this packages are : Biweight kernel, Epanechnikov kernel, Rectangular kernel, Triangular kernel and the truncated Gaussian kernel.
LowBound |
the lower bound of the bootstrap (1-alpha)-confidence interval. |
UppBound |
the upper bound of the bootstrap (1-alpha)-confidence interval of level. |
The executing time of the function can be time consuming if the B parameter or the sample size are high (B=100 and the sample size = 5000 for example) .
theta <- function(t){
0.5+0.25*sin(2*pi*t)
}
n <- 5000
t <- 1:n/n
Theta <- theta(t)
set.seed(123)
Data <- NULL
for(i in 1:n){
Data[i] <- rparetomix(1, a = 1/Theta[i], b = 1/Theta[i]+5, c = 0.75)
}
Tgrid <- seq(1, length(Data)-1, length = 20)/n
h <- 0.1
## Not run: #For computing time purpose
bootCI.ts(Data, t, Tgrid, h, kernel = TruncGauss.kernel, kpar = c(sigma = 1),
CritVal = 3.6, threshold = 2, type = "survival", B = 100, plot = TRUE)
true.p <- NULL
for(i in 1:n){
true.p[i] <- 1-pparetomix(2, a = 1/Theta[i], b = 1/Theta[i]+5, c = 0.75)
}
lines(t, true.p, col = "red")
bootCI.ts(Data, t, Tgrid, h, kernel = TruncGauss.kernel, kpar = c(sigma = 1),
prob = 0.999, type = "quantile", B = 100, plot = TRUE)
true.quantile <- NULL
for(i in 1:n){
true.quantile[i] <- qparetomix(0.999, a = 1/Theta[i], b = 1/Theta[i]+5, c = 0.75)
}
lines(t, log(true.quantile), col = "red")
## End(Not run)Please choose more modern alternatives, such as Google Chrome or Mozilla Firefox.