Asymptotic normality of the mixture density estimator in a disaggregation scheme

TL;DR

This paper proves that the mixture density estimator used in disaggregation of random parameter AR(1) processes is asymptotically normal under mild conditions, supported by theoretical proof and simulation.

Contribution

It establishes the asymptotic normality of the mixture density estimator in a semiparametric disaggregation framework, extending previous results.

Findings

Estimator is asymptotically normal under mild conditions

Theoretical proof based on quadratic form limit theory

Simulation study confirms the theoretical results

Abstract

The paper concerns the asymptotic distribution of the mixture density estimator, proposed by Oppenheim et al 2006, in the aggregation/disaggregation problem of random parameter AR(1) process. We prove that, under mild conditions on the (semiparametric) form of the mixture density, the estimator is asymptotically normal. The proof is based on the limit theory for the quadratic form in linear random variables developed by Bhansali et al 2007. The moving average representation of the aggregated process is investigated. A small simulation study illustrates the result.