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Strong pointwise consistency of the kT -occupation time density estimator

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  • Labrador, Boris

Abstract

In this paper, we study the kT-occupation time density estimator as an extension of the k-nearest neighbor estimator in continuous time. The rates of strong pointwise convergence for [alpha]-mixing and bounded processes in both optimal (when i.i.d. rates of density estimation are reached) and superoptimal cases (when parametric rates are reached) are established.

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  • Labrador, Boris, 2008. "Strong pointwise consistency of the kT -occupation time density estimator," Statistics & Probability Letters, Elsevier, vol. 78(9), pages 1128-1137, July.
    • Handle: RePEc:eee:stapro:v:78:y:2008:i:9:p:1128-1137
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    1. Blanke, D. & Bosq, D., 1997. "Accurate rates of density estimators for continuous-time processes," Statistics & Probability Letters, Elsevier, vol. 33(2), pages 185-191, April.
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    3. Tran, L. T. & Yakowitz, S., 1993. "Nearest Neighbor Estimators for Random Fields," Journal of Multivariate Analysis, Elsevier, vol. 44(1), pages 23-46, January.
    4. Deheuvels, Paul, 1992. "Functional laws of the iterated logarithm for large increments of empirical and quantile processes," Stochastic Processes and their Applications, Elsevier, vol. 43(1), pages 133-163, November.
    5. Boente, Graciela & Fraiman, Ricardo, 1988. "Consistency of a nonparametric estimate of a density function for dependent variables," Journal of Multivariate Analysis, Elsevier, vol. 25(1), pages 90-99, April.
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    Cited by:

    1. Liliana Forzani & Ricardo Fraiman & Pamela Llop, 2013. "Density estimation for spatial-temporal models," TEST: An Official Journal of the Spanish Society of Statistics and Operations Research, Springer;Sociedad de Estadística e Investigación Operativa, vol. 22(2), pages 321-342, June.
    2. Llop, P. & Forzani, L. & Fraiman, R., 2011. "On local times, density estimation and supervised classification from functional data," Journal of Multivariate Analysis, Elsevier, vol. 102(1), pages 73-86, January.

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