Deconvolution of a Distribution Function

Abstract

We consider the estimation of a distribution function when observations from this distribution are contaminated by measurement error. The unknown distribution is modeled as a mixture of a finite number of known distributions. Model parameters can be estimated and confidence intervals constructed using well-known likelihood theory. We show that it is also possible to apply this approach to estimation of a unimodal distribution. An application is presented using data from a dietary survey. Simulation results are given to indicate the performance of the estimators and the confidence interval procedures.

Key Words:

• Expectation-maximization algorithm
• Mixture of distributions
• Profile likelihood
• Unimodal distribution.