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

G. Jogesh Babu, Yogendra P. Chaubey

Research output: Contribution to journalArticle

23 Citations (Scopus)

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 [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.

Original languageEnglish (US)
Pages (from-to)959-969
Number of pages11
JournalStatistics and Probability Letters
Volume76
Issue number9
DOIs
StatePublished - May 1 2006

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Bernstein Polynomials
Random Vector
Hypercube
Density Function
Distribution Function
Estimator
Dependent
Conditional Density
Strong Consistency
Nonlinear Dynamical Systems
Asymptotic Normality
Asymptotic Properties
Smoothness
Continuous Function
Density function
Distribution function
Polynomials

All Science Journal Classification (ASJC) codes

  • Statistics, Probability and Uncertainty
  • Statistics and Probability

Cite this

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Smooth estimation of a distribution and density function on a hypercube using Bernstein polynomials for dependent random vectors. / Babu, G. Jogesh; Chaubey, Yogendra P.

In: Statistics and Probability Letters, Vol. 76, No. 9, 01.05.2006, p. 959-969.

Research output: Contribution to journalArticle

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