R/plain.R

In jrzubizarreta/scbounds: Shape-constrained partial identification of a population mean under unknown probabilities of sample selection

#' Computes upper identification interval without shape constraints, as
#' in Aronow & Lee (2013).
#' 
#' @param X The observed data.
#' @param sampling.ratio Bound on the sampling weights gamma.
#' @param xmin Used to construct histogram representation.
#' @param xmax Used to construct histogram representation.
#' @param buckets Used to construct histogram representation.
#' 
#' @return mu.bound The upper bound for mu(x).
#' 
#' @return Xhat Unweighted empirical CDF of the data.
#' @return xvals Points at which Xhat is evaluated.
#' @return Xhat.weighted Weighted version of Xhat that maximizes mu, subject to sampling ratio constraint.
#' 
#' @export bounds.plain.internal
bounds.plain.internal = function(X, sampling.ratio = 5,
                                 xmin = NULL, xmax = NULL, buckets = 1000) {
  
  n = length(X)
  
  if(is.null(xmin)) { xmin = min(X) }
  if(is.null(xmax)) { xmax = max(X) }
  
  if(xmin > min(X) | xmax < max(X)) { stop ("support too short") }
  
  xvals = seq(xmin, xmax, length.out = buckets + 1)
  
  Xhat = ecdf(X)(xvals)
  Xhat.AL = hajek.constrained(Xhat, xvals, sampling.ratio)
  
  mu.bound = sum(xvals * (Xhat.AL - c(0, Xhat.AL[-length(Xhat.AL)])))
  
  ret = list(mu.bound=mu.bound,
             raw=data.frame(
               xvals=xvals,
               Xhat=Xhat,
               Xhat.weighted=Xhat.AL
             ))
  
  return(ret)
}