Asymptotic normality of the mixture density estimator in a disaggregation scheme

Dmitrij Celov (1) , Remigijus Leipus (1) , Anne Philippe (2)

1 Vilnius Institute of Mathematics and Informatics
2 LMJL - Laboratoire de Mathématiques Jean Leray

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.

Mots clés: random coefficient AR(1); long memory; aggregation; disaggregation

Domaines: Statistiques [math.ST]

Dmitrij Celov, Remigijus Leipus, Anne Philippe. Asymptotic normality of the mixture density estimator in a disaggregation scheme. 2008. ⟨hal-00242913⟩