• xmlui.mirage2.page-structure.header.title
    • français
    • English
  • Help
  • Login
  • Language 
    • Français
    • English
View Item 
  •   BIRD Home
  • CEREMADE (UMR CNRS 7534)
  • CEREMADE : Publications
  • View Item
  •   BIRD Home
  • CEREMADE (UMR CNRS 7534)
  • CEREMADE : Publications
  • View Item
JavaScript is disabled for your browser. Some features of this site may not work without it.

Browse

BIRDResearch centres & CollectionsBy Issue DateAuthorsTitlesTypeThis CollectionBy Issue DateAuthorsTitlesType

My Account

LoginRegister

Statistics

Most Popular ItemsStatistics by CountryMost Popular Authors
Thumbnail

Consistent estimation of a convex density at the origin

Balabdaoui, Fadoua (2007), Consistent estimation of a convex density at the origin, Mathematical Methods of Statistics, 16, 2, p. 77-95. http://dx.doi.org/10.3103/S1066530707020019

View/Open
plugin-2007-22.pdf (561.3Kb)
Type
Article accepté pour publication ou publié
Date
2007
Journal name
Mathematical Methods of Statistics
Volume
16
Number
2
Publisher
Allerton Press, Inc.
Pages
77-95
Publication identifier
http://dx.doi.org/10.3103/S1066530707020019
Metadata
Show full item record
Author(s)
Balabdaoui, Fadoua
Abstract (EN)
Motivated by Hampel's birds migration problem, \mycite{gjw:01b} established the asymptotic distribution theory for the nonparametric Least Squares and Maximum Likelihood estimators of a convex and decreasing density, $g_0$, at a fixed point $t_0 > 0$. However, estimation of the distribution function of the birds' resting times involves estimation of $g'_0$ at 0, a boundary point at which the estimators are not consistent. In this paper, we focus on the Least Squares estimator, $\tilde{g}_n$. Our goal is to show that consistent estimators of both $g_0(0)$ and $g'_0(0)$ can be based solely on $\tilde{g}_n$. Following the idea of \mycite{kuliandlopuh:06} in monotone estimation, we show that it suffices to take $\tilde{g}_n(n^{-\alpha})$ and $\tilde{g}'_n(n^{-\alpha})$, with $\alpha \in (0,1/3)$. We establish their joint asymptotic distributions and show that $\alpha =1/5$ should be taken as it yields the fastest rates of convergence.
Subjects / Keywords
Convex density; Hampel's problem; estimation at the boundary; Brownian motion

Related items

Showing items related by title and author.

  • Thumbnail
    Estimation of a k-monotone density: limit distribution theory and the Spline connection 
    Balabdaoui, Fadoua; Wellner, Jon (2007) Article accepté pour publication ou publié
  • Thumbnail
    Limit distribution theory for maximum likelihood estimation of a log-concave density 
    Balabdaoui, Fadoua; Rufibach, Kaspar; Wellner, Jon (2009) Article accepté pour publication ou publié
  • Thumbnail
    Estimation of a k-monotone density: characterizations, consistency and minimax lower bounds 
    Wellner, Jon; Balabdaoui, Fadoua (2010) Article accepté pour publication ou publié
  • Thumbnail
    Marshall lemma in discrete convex estimation 
    Balabdaoui, Fadoua; Durot, Cécile (2015) Article accepté pour publication ou publié
  • Thumbnail
    A second Marshall inequality in convex estimation 
    Rufibach, Kaspar; Balabdaoui, Fadoua (2008) Article accepté pour publication ou publié
Dauphine PSL Bibliothèque logo
Place du Maréchal de Lattre de Tassigny 75775 Paris Cedex 16
Phone: 01 44 05 40 94
Contact
Dauphine PSL logoEQUIS logoCreative Commons logo