The Annals of Statistics

Nonparametric Probability Density Estimation by Discrete Maximum Penalized- Likelihood Criteria

D. W. Scott, R. A. Tapia, and J. R. Thompson

Full-text: Open access

Abstract

A nonparametric probability density estimator is proposed that is optimal with respect to a discretized form of a continuous penalized-likelihood criterion functional. Approximation results relating the discrete estimator to the estimate obtained by solving the corresponding infinite-dimensional problem are presented. The discrete estimator is shown to be consistent. The numerical implementation of this discrete estimator is outlined and examples displayed. A simulation study compares the integrated mean square error of the discrete estimator with that of the well-known kernel estimators. Asymptotic rates of convergence of the discrete estimator are also investigated.

Article information

Source
Ann. Statist., Volume 8, Number 4 (1980), 820-832.

Dates
First available in Project Euclid: 12 April 2007

Permanent link to this document
https://projecteuclid.org/euclid.aos/1176345074

Digital Object Identifier
doi:10.1214/aos/1176345074

Mathematical Reviews number (MathSciNet)
MR572625

Zentralblatt MATH identifier
0438.62034

JSTOR
links.jstor.org

Keywords
G2G05 G2E10 Nonparametric density estimation maximum likelihood estimation kernel density estimation

Citation

Scott, D. W.; Tapia, R. A.; Thompson, J. R. Nonparametric Probability Density Estimation by Discrete Maximum Penalized- Likelihood Criteria. Ann. Statist. 8 (1980), no. 4, 820--832. doi:10.1214/aos/1176345074. https://projecteuclid.org/euclid.aos/1176345074


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