L2Version Of The Double Kernel Method
Author:
- 1 January 1999
- journal article
- research article
- Published by Taylor & Francis in Statistics
- Vol. 32 (3) , 249-266
Abstract
Consider two kernel density estimates having the same bandwidth but two different kernels. The criterion which minimizes the L 1 distance between these two estimates is known as the double kernel method. In this work, instead of the L 1 distance, we use the L 2 one. Asymptotic behavior of this criterion and the corresponding bandwidth are investigated. It is shown that the L 2 double kernel method and the least-squares cross-validation technique have almost the same properties. An implementation of the method is also proposed.Keywords
This publication has 17 references indexed in Scilit:
- Computationally efficient classes of higher‐order kernel functionsCanadian Journal of Statistics, 1995
- A comparative study of some bias correction techniques for kernel- based density estimatorsJournal of Statistical Computation and Simulation, 1995
- A comparative study of several smoothing methods in density estimationComputational Statistics & Data Analysis, 1994
- Hierarchies of higher order kernelsProbability Theory and Related Fields, 1993
- Generalized jackknifing and higher order kernelsJournal of Nonparametric Statistics, 1993
- Smoothed cross-validationProbability Theory and Related Fields, 1992
- A Simple Root $n$ Bandwidth SelectorThe Annals of Statistics, 1991
- Central limit theorem for integrated square error of multivariate nonparametric density estimatorsJournal of Multivariate Analysis, 1984
- On Estimation of a Probability Density Function and ModeThe Annals of Mathematical Statistics, 1962
- Remarks on Some Nonparametric Estimates of a Density FunctionThe Annals of Mathematical Statistics, 1956