Nothing
ISEL_legendre <- function(gam, w, knots, t.alpha,
nodes, weights, s.spl){
# Computes the inner integral of the scaled expected
# length 1 and 2 of Kabaila and Giri confidence interval.
# The integral from (0, d) is broken down to integrals
# over knots. Each integral is computed using gauss
# legendre quadrature. The number of nodes and weights
# for the approximation of each integral can be changed.
#
# Inputs:
# gam: parameter
# w: a value of the variable of integration in the
# outer integral
# knots: location of knots in [0, d]
# t.alpha: quantile of the t distribution for m and alpha
# nodes: vector of Gauss Legendre quadrature nodes
# weights: vector of Gauss Legendre quadrature weights
# s.spl: s function
#
# Output:
# A value for the inner integral of the scaled expected
# length 1 and 2
#
# Written by N.Ranathunga in September 2020.
# Set up a vector to store the results
int <- rep(0, length(knots))
for(i in 1:(length(knots) - 1)){
# Specify bounds of the integral
a <- knots[i]
b <- knots[i+1]
# Find the approximate integral
adj.nodes <- ((b - a) / 2) * nodes + (a + b) / 2
q <- IISEL(adj.nodes, gam, w, t.alpha, s.spl)
int[i] <- ((b - a) / 2) * sum(weights * q)
}
ISEL <- sum(int)
}
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