Nonparametric likelihood based estimation for a multivariate Lipschitz density

Daniel Carando, Ricardo Fraiman and Pablo Groisman

Journal of Multivariate Analysis, 2009, vol. 100, issue 5, 981-992

Abstract: We consider a problem of nonparametric density estimation under shape restrictions. We deal with the case where the density belongs to a class of Lipschitz functions. Devroye [L. Devroye, A Course in Density Estimation, in: Progress in Probability and Statistics, vol. 14, Birkhuser Boston Inc., Boston, MA, 1987] considered these classes of estimates as tailor-made estimates, in contrast in some way to universally consistent estimates. In our framework we get the existence and uniqueness of the maximum likelihood estimate as well as strong consistency. This NPMLE can be easily characterized but it is not easy to compute. Some simpler approximations are also considered.

Keywords: primary; 62G07 secondary; 62F30; 62G20 Density estimation Maximum likelihood Tailor-made estimates (search for similar items in EconPapers)
Date: 2009
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Citations: View citations in EconPapers (2)

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