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A note on density estimation for binary sequences

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  • Bharath, Karthik

Abstract

A histogram estimate of the Radon–Nikodym derivative of a probability measure with respect to a dominating measure is developed for binary sequences in {0,1}N. A necessary and sufficient condition for the consistency of the estimate in the mean-square sense is given. It is noted that the product topology on {0,1}N and the corresponding dominating product measure pose considerable restrictions on the rate of sampling required for the requisite convergence.

Suggested Citation

  • Bharath, Karthik, 2013. "A note on density estimation for binary sequences," Statistics & Probability Letters, Elsevier, vol. 83(12), pages 2735-2742.
    • Handle: RePEc:eee:stapro:v:83:y:2013:i:12:p:2735-2742
    DOI: 10.1016/j.spl.2013.09.013
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    References listed on IDEAS

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    1. Angelika Linde, 2009. "A Bayesian latent variable approach to functional principal components analysis with binary and count data," AStA Advances in Statistical Analysis, Springer;German Statistical Society, vol. 93(3), pages 307-333, September.
    2. David Balding & Pablo Ferrari & Ricardo Fraiman & Mariela Sued, 2009. "Limit theorems for sequences of random trees," TEST: An Official Journal of the Spanish Society of Statistics and Operations Research, Springer;Sociedad de Estadística e Investigación Operativa, vol. 18(2), pages 302-315, August.
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