The Annals of Statistics

Asymptotic Analysis of Penalized Likelihood and Related Estimators

Dennis D. Cox and Finbarr O'Sullivan

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Abstract

A general approach to the first order asymptotic analysis of penalized likelihood and related estimators is described. The method gives expansions for the systematic and random error. Asymptotic convergence rates in a family of spectral norms are obtained. The theory applies to a broad range of function estimation problems including nonparametric density, hazard and generalized regression curve estimation. Some examples are provided.

Article information

Source
Ann. Statist., Volume 18, Number 4 (1990), 1676-1695.

Dates
First available in Project Euclid: 12 April 2007

Permanent link to this document
https://projecteuclid.org/euclid.aos/1176347872

Digital Object Identifier
doi:10.1214/aos/1176347872

Mathematical Reviews number (MathSciNet)
MR1074429

Zentralblatt MATH identifier
0719.62051

JSTOR
links.jstor.org

Subjects
Primary: 62G05: Estimation
Secondary: 62J05: Linear regression 41A35: Approximation by operators (in particular, by integral operators) 41A25: Rate of convergence, degree of approximation 47A53: (Semi-) Fredholm operators; index theories [See also 58B15, 58J20] 45L10 45M05: Asymptotics

Keywords
Linearization spectral analysis rates of convergence

Citation

Cox, Dennis D.; O'Sullivan, Finbarr. Asymptotic Analysis of Penalized Likelihood and Related Estimators. Ann. Statist. 18 (1990), no. 4, 1676--1695. doi:10.1214/aos/1176347872. https://projecteuclid.org/euclid.aos/1176347872


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