Self-concordant empirical likelihood for a vector mean

Self-concordant empirical likelihood for a vector mean

Usage

emplik(
  dat,
  mu = rep(0, ncol(dat)),
  lam = rep(0, ncol(dat)),
  eps = 1/nrow(dat),
  M = 1e+30,
  thresh = 1e-30,
  itermax = 100
)

Arguments

dat

n by d matrix of d-variate observations

mu

d vector of hypothesized mean of dat

lam

starting values for Lagrange multiplier vector, default to zero vector

eps

lower cutoff for \(-\log\), with default 1/nrow(dat)

M

upper cutoff for \(-\log\).

thresh

convergence threshold for log likelihood (default of 1e-30 is aggressive)

itermax

upper bound on number of Newton steps.

Value

a list with components

• logelr log empirical likelihood ratio.

• lam Lagrange multiplier (vector of length d).

• wts n vector of observation weights (probabilities).

• conv boolean indicating convergence.

• niter number of iteration until convergence.

• ndec Newton decrement.

• gradnorm norm of gradient of log empirical likelihood.

References

Owen, A.B. (2013). Self-concordance for empirical likelihood, Canadian Journal of Statistics, 41(3), 387–397.

Author

Art Owen, C++ port by Leo Belzile