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ON THE GRENANDER ESTIMATOR AT ZERO.

Fadoua Balabdaoui1, Hanna Jankowski, Marios Pavlides

  • 1Centre de Recherche en Mathématiques de la Décision, Université Paris-Dauphine, Paris, 75775, France.

Statistica Sinica
|June 21, 2011
PubMed
Summary
This summary is machine-generated.

We establish limit theory for the Grenander estimator of monotone densities, especially when the density is unbounded near zero. New switching relations from convex analysis are developed and applied to mixture problems.

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Area of Science:

  • Statistics
  • Mathematical Analysis

Background:

  • The Grenander estimator is used for estimating monotone functions.
  • Understanding its behavior near zero, particularly with unbounded densities, is crucial for statistical inference.

Purpose of the Study:

  • To establish the limit theory for the Grenander estimator of a monotone density near zero.
  • To analyze cases where the true density is unbounded at zero with varying growth rates.

Main Methods:

  • Development of new switching relations using convex analysis tools.
  • Application of established limit theory principles to density estimation.

Main Results:

  • The study establishes the limit theory for the Grenander estimator under specific conditions near zero.
  • New switching relations were successfully developed and utilized.

Conclusions:

  • The findings provide a theoretical framework for Grenander estimation with unbounded densities.
  • The developed theory has practical implications, demonstrated by its application to mixture problems.