Asymptotic normality of the mixture density estimator in a disaggregation scheme

2008/02/06 by Dmitrij Celov, Celov, Dmitrij, Remigijus Leipus +3
Computer Science · Mathematics · #Advanced Statistical Methods and Models #Bayesian Methods and Mixture Models #FOS: Mathematics #Statistical Methods and Inference #Statistics Theory (math.ST) #math.ST #stat.TH

paper · pdf · doi:10.48550/arxiv.0802.0817

arxiv created 2008/02/06 · openalex publication_date 2008/02/06 · arxiv updated 2009/12/01 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

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.

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