Article ID | Journal | Published Year | Pages | File Type |
---|---|---|---|---|
1149466 | Journal of Statistical Planning and Inference | 2011 | 11 Pages |
Abstract
We investigate the problem of estimating a smooth invertible transformation f when observing independent samples X1,â¦,Xnâ¼Pâf where P is a known measure. We focus on the two-dimensional case where P and f are defined on R2. We present a flexible class of smooth invertible transformations in two dimensions with variational equations for optimizing over the classes, then study the problem of estimating the transformation f by penalized maximum likelihood estimation. We apply our methodology to the case when Pâf has a density with respect to Lebesgue measure on R2 and demonstrate improvements over kernel density estimation on three examples.
Related Topics
Physical Sciences and Engineering
Mathematics
Applied Mathematics
Authors
Ethan Anderes, Marc A. Coram,