Estimation de densités unimodales
Author:
- 1 September 1997
- journal article
- Published by Wiley in Canadian Journal of Statistics
- Vol. 25 (3) , 375-387
Abstract
This paper proposes a new nonparametric unimodal estimator of a unimodal probability density function, in the case where the mode is known. The classical solution to this problem is the maximum‐likelihood estimator under monotonicity constraint, considered by Grenander (1956). Our approach is based on a unimodal rearrangement of the kernel estimator of the density. Asymptotic properties of this estimator are studied, and its small‐sample behaviour is examined through simulations.Keywords
This publication has 7 references indexed in Scilit:
- A minimax optimal estimator for continuous monotone densitiesJournal of Statistical Planning and Inference, 1995
- TheL1theory of estimation of monotone and unimodal densitiesJournal of Nonparametric Statistics, 1995
- The Grenader Estimator: A Nonasymptotic ApproachThe Annals of Statistics, 1989
- Brownian motion with a parabolic drift and airy functionsProbability Theory and Related Fields, 1989
- Extreme Values, Regular Variation and Point Processes1987
- Asymptotic Normality of Statistics Based on the Convex Minorants of Empirical Distribution FunctionsThe Annals of Probability, 1983
- An approximation of partial sums of independent RV'-s, and the sample DF. IProbability Theory and Related Fields, 1975