Smooth estimation of a distribution and density function on a hypercube using Bernstein polynomials for dependent random vectors

G. Jogesh Babu and Yogendra P. Chaubey

Statistics & Probability Letters, 2006, vol. 76, issue 9, 959-969

Abstract: This paper considers multivariate extension of smooth estimator of the distribution and density function based on Bernstein polynomials studied in Babu et al. [2002. Application of Bernstein polynomials for smooth estimation of a distribution and density function. J. Statist. Plann. Inference 105, 377-392]. Multivariate version of Bernstein polynomials for approximating a bounded and continuous function is considered and adapted for smooth estimation of a distribution function concentrated on the hypercube . The smoothness of the resulting estimator, naturally lends itself in a smooth estimator of the corresponding density. The functions with other compact or non-compact support can be dealt through suitable transformations. The asymptotic properties, namely, strong consistency and asymptotic normality of the resulting estimators are investigated under [alpha]-mixing. This has been motivated by estimation of conditional densities in non-linear dynamical systems.

Keywords: Asymptotic; normality; Kernel; estimator; Non-parametric; density; estimation; Strong; consistency; Strong; mixing (search for similar items in EconPapers)
Date: 2006
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Citations: View citations in EconPapers (14)

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