Estimating a frequency distribution when the sampling is biased
COMMUNICATIONS IN STATISTICS-THEORY AND METHODS | MARCEL DEKKER INC | Published : 1999
A simple random sample on a random variable X allows its density to be consistently estimated, by a histogram or preferably a kernel density estimate. When the sampling is biased towards certain x-values these methods instead estimate a weighted version of the density function. This article proposes a method for estimating both the density and the sampling bias simultaneously. The technique requires two independent samples and utilises ideas from mark-recapture experiments. An estimator of the size of the sampled population also follows simply from this density estimate. Copyright © 1999 by Marcel Dekker, Inc.