Weibullmix: NPMLE for Weibull Mixtures

Description

Kiefer-Wolfowitz NPMLE for Weibull Mixtures of scale parameter

Usage

Weibullmix(
  x,
  v = 300,
  u = 300,
  alpha,
  lambda = 1,
  event = NULL,
  hist = FALSE,
  weights = NULL,
  ...
)

Value

An object of class density with components

x: points of evaluation on the domain of the density
y: estimated function values at the points x of the mixing density
logLik: Log likelihood value at the proposed solution
dy: Bayes Rule estimates of mixing parameter
status: exit code from the optimizer

Arguments

x: Survival times
v: Grid values for mixing distribution
u: Grid values for histogram bins, if needed
alpha: Shape parameter for Weibull distribution
lambda: Scale parameter for Weibull Distribution; must either have length 1, or length equal to length(x) the latter case accommodates the possibility of a linear predictor
event: censoring indicator, 1 if actual event time, 0 if censored
hist: If TRUE aggregate to histogram counts
weights: replicate weights for x obervations, should sum to 1
...: optional parameters passed to KWDual to control optimization

Author

Roger Koenker and Jiaying Gu

Details

Kiefer Wolfowitz NPMLE density estimation for Weibull scale mixtures. The histogram option is intended for relatively large problems, say n > 1000, where reducing the sample size dimension is desirable. By default the grid for the binning is equally spaced on the support of the data. Parameterization: f(t|alpha, lambda) = alpha * exp(v) * (lambda * t )^(alpha-1) * exp(-(lambda * t)^alpha * exp(v)); shape = alpha; scale = lambda^(-1) * (exp(v))^(-1/alpha) This version purports to handle right censoring.

References

Kiefer, J. and J. Wolfowitz Consistency of the Maximum Likelihood Estimator in the Presence of Infinitely Many Incidental Parameters Ann. Math. Statist. Volume 27, Number 4 (1956), 887-906.

Koenker, R. and J. Gu, (2017) REBayes: An R Package for Empirical Bayes Mixture Methods, Journal of Statistical Software, 82, 1--26.