Two Dimensional Density Estimation using Smooth Invertible Transformations

Details Two Dimensional Density Estimation using Smooth Invertible Transformations Two Dimensional Density Estimation using Smooth Invertible Transformations

2008-07-14

arxiv.org/abs/0807.2275v1

Statistics

Methodology

Scientific paper

We investigate the problem of estimating a smooth invertible transformation f when observing independent samples X_1, ..., X_n ~ P \circ f, where P is a known measure. We focus on the two dimensional case where P and f are defined on R^2. 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 P \circ f has a density with respect to Lebesgue measure on R^2 and demonstrate improvements over kernel density estimation on three examples.

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