TY - JOUR

T1 - Smooth estimation of a distribution and density function on a hypercube using Bernstein polynomials for dependent random vectors

AU - Babu, G. Jogesh

AU - Chaubey, Yogendra P.

N1 - Funding Information:
This research work is supported in part by Yogendra P. Chaubey's NSERC of Canada Grant, and G. Jogesh Babu's National Science Foundation Grant AST-0434234. The authors would also like to thank a referee whose suggestions have resulted in an improved version of the paper.

PY - 2006/5/1

Y1 - 2006/5/1

N2 - 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 [0, 1]d, d > 1. 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 α-mixing. This has been motivated by estimation of conditional densities in non-linear dynamical systems.

AB - 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 [0, 1]d, d > 1. 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 α-mixing. This has been motivated by estimation of conditional densities in non-linear dynamical systems.

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U2 - 10.1016/j.spl.2005.10.031

DO - 10.1016/j.spl.2005.10.031

M3 - Article

AN - SCOPUS:33645537171

VL - 76

SP - 959

EP - 969

JO - Statistics and Probability Letters

JF - Statistics and Probability Letters

SN - 0167-7152

IS - 9

ER -