Order
restricted semiparametric inference for the power bias model
Ori Davidov, Konstantinos Fokianos and George
Iliopoulos
The
power bias model, a generalization of length biased sampling, is introduced and
investigated in detail. In particular, attention is focused on order restricted
inference. We show that the power bias model is an example of the density ratio
model, or in other words, it is a semiparametric model which is specified by assuming that the
ratio of several unknown probability density functions has a parametric
from. Estimation and testing procedures
under constraints are developed in detail. It is shown that the power bias
model can be used for testing for, or against, the likelihood ratio ordering
among multiple populations without resorting to any parametric assumptions.
Examples and real data analysis demonstrate the usefulness of this approach.
Key words and phrases: Biased sampling;
empirical likelihood; likelihood ratio ordering; PAVA algorithm; semiparametric
models; tree order; stochastic order.