Abstract
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.
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