compute_AEL {VBel}

Compute the Adjusted Empirical Likelihood

Description

Evaluates the AEL for a given data set, moment conditions and parameter values

Usage

compute_AEL(th, h, lam0, a, z, iters, useR_forz, returnH)

Arguments

th

Vector or scalar theta

h

User-defined function, outputs array

lam0

Initial vector for lambda

a

Scalar constant

z

n-1 by d matrix

iters

Number of iterations using Newton-Raphson for estimation of lambda (default: 500)

useR_forz

Bool whether to calculate the function first in R (True) or call the function in C (False) (default: True)

returnH

Whether to return calculated values of h, H matrix and lambda

Value

A numeric value for the Adjusted Empirical Likelihood function computed evaluated at a given theta value

Author(s)

Wei Chang Yu, Jeremy Lim

References

Yu, W., & Bondell, H. D. (2023). Variational Bayes for Fast and Accurate Empirical Likelihood Inference. Journal of the American Statistical Association, 1–13. doi:10.1080/01621459.2023.2169701

Examples

# Generate toy variables
set.seed(1)
x     <- runif(30, min = -5, max = 5)
elip  <- rnorm(30, mean = 0, sd = 1)
y     <- 0.75 - x + elip

# Set initial values for AEL computation
lam0  <- matrix(c(0,0), nrow = 2)
th    <- matrix(c(0.8277, -1.0050), nrow = 2)
a     <- 0.00001
iters <- 10

# Define Dataset and h-function
z <- cbind(x, y)
h <- function(z, th) {
    xi      <- z[1]
    yi      <- z[2]
    h_zith  <- c(yi - th[1] - th[2] * xi, xi*(yi - th[1] - th[2] * xi))
    matrix(h_zith, nrow = 2)
}
ansAELRcpp <- compute_AEL(th, h, lam0, a, z, iters, useR_forz = TRUE)