A study of logspline density estimation

A method of estimating an unknown density function ƒ based on sample data is studied. Our approach is to use maximum likelihood etimation to estimate log(ƒ) by a function s from a space of cubic splines that have a finite number of prespecified knots and are linear in the tails. The knots are placed...

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Bibliographic Details
Published in:Computational statistics & data analysis 1991, Vol.12 (3), p.327-347
Main Authors: Kooperberg, Charles, Stone, Charles J.
Format: Article
Language:English
Subjects:
AIC
Density estimation
Exact sciences and technology
Exponential family
Mathematics
Probability and statistics
Sciences and techniques of general use
Splines
Statistics
Stepwise knot deletion
Transformations
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Summary:A method of estimating an unknown density function ƒ based on sample data is studied. Our approach is to use maximum likelihood etimation to estimate log(ƒ) by a function s from a space of cubic splines that have a finite number of prespecified knots and are linear in the tails. The knots are placed at selected order statistics of the sample data. The number of knots can be determined either by a simple rule or by minimizing a variant of AIC. Examples using both simulated and real data show that the method works well both in obtaining smooth estimates and in picking up small details. The method is fully automatic and can easily be extended to yield estimates and confidence bounds for quantiles.
ISSN:0167-9473
1872-7352
DOI:10.1016/0167-9473(91)90115-I