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Asymptotic properties of Bernstein estimators on the simplex

Ouimet, Frédéric (2020) Asymptotic properties of Bernstein estimators on the simplex. . (Unpublished)

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In this paper, we study various asymptotic properties (bias, variance, mean squared error, mean integrated squared error, asymptotic normality, uniform strong consistency) for Bernstein estimators of cumulative distribution functions and density functions on the d-dimensional simplex. Our results generalize the ones in Leblanc (2012) and Babu et al. (2002), which treated the case d=1, and significantly extend those found in Tenbusch (1994) for the density estimators when d=2. The density estimator (or smoothed histogram) is closely related to the Dirichlet kernel estimator from Ouimet (2020), and can also be used to analyze compositional data.

Item Type:Report or Paper (Discussion Paper)
Related URLs:
URLURL TypeDescription Paper
Ouimet, Frédéric0000-0001-7933-5265
Additional Information:1F. O. is supported by a postdoctoral fellowship from the NSERC (PDF) and the FRQNT (B3X supplement). Preprint submitted to Elsevier.
Funding AgencyGrant Number
Natural Sciences and Engineering Research Council of Canada (NSERC)UNSPECIFIED
Fonds de recherche du Québe-Nature et technologies (FRQ-NT)UNSPECIFIED
Subject Keywords:Bernstein estimators, simplex, cumulative distribution function estimation, density estimation, mean squared error, asymptotic normality, uniform strong consistency
Classification Code:2010 MSC: Primary : 62G07 Secondary : 62G05, 62G20
Record Number:CaltechAUTHORS:20200309-105256028
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Usage Policy:No commercial reproduction, distribution, display or performance rights in this work are provided.
ID Code:101773
Deposited By: Joy Painter
Deposited On:09 Mar 2020 20:44
Last Modified:09 Mar 2020 20:44

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