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On the Estimation of a Probability Density Function by the Maximum Penalized Likelihood Method
Open accessAbstract
A class of probability density estimates can be obtained by penalizing the likelihood by a functional which depends on the roughness of the logarithm of the density. The limiting case of the estimates as the amount of smoothing increases has a natural form which makes the method attractive for data analysis and which provides a rationale for a particular choice of roughness penalty. The estimates are shown to be the solution of an unconstrained convex optimization problem, and mild natural conditions are given for them to exist. Rates of consistency in various norms and conditions for asymptotic normality and approximation by a Gaussian process are given, thus breaking new ground in the theory of maximum penalized likelihood density estimation.
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Citations
Cited by
Some aspects of the spline smoothing approach to non-parametric regression curve fitting
Silverman, B. W. (1985) · Journal of the Royal Statistical Society Series B: Statistical Methodology · doi:10.1111/j.2517-6161.1985.tb01327.x · Cited by 1,117
Self-citationApplied Functional Data Analysis: Methods and Case Studies
(2002) · Springer Series in Statistics · doi:10.1007/b98886 · Cited by 787
Risk bounds for model selection via penalization
Barron, A., Birgé, L., & Massart, P. (1999) · Probability Theory and Related Fields · doi:10.1007/s004400050210 · Cited by 657
Regression, Prediction and Shrinkage
Copas, J. B. (1983) · Journal of the Royal Statistical Society Series B: Statistical Methodology · doi:10.1111/j.2517-6161.1983.tb01258.x · Cited by 612
Applied Functional Data Analysis
Altland, H. W. (2003) · Technometrics · doi:10.1198/tech.2003.s16 · Cited by 494
Metadata
- Authors
- Silverman, B. W.
- Venue
- The Annals of Statistics
- Publisher
- Institute of Mathematical Statistics
- Published
- 1982-09-01
- Volume
- 10
- Issue
- 3
- ISSN
- 0090-5364 (ISSN-L)
- OpenAlex
- W2020914331
- Cited by
- 305
- References
- 0
- FWCI
- 5.69
- Type
- journal article
- Language
- en
- Open access
- bronze
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- Silverman, B. W. (1982). On the Estimation of a Probability Density Function by the Maximum Penalized Likelihood Method. The Annals of Statistics. https://doi.org/10.1214/aos/1176345872
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