# Nonparametric density estimation by histogram trend filtering

@article{Padilla2015NonparametricDE, title={Nonparametric density estimation by histogram trend filtering}, author={Oscar Hernan Madrid Padilla and James G. Scott}, journal={arXiv: Methodology}, year={2015} }

We propose a novel approach for density estimation called histogram trend filtering. Our estimator arises from looking at surrogate Poisson model for counts of observations in a partition of the support of the data. We begin by showing consistency for a variational estimator for this density estimation problem. We then study a discrete estimator that can be efficiently found via convex optimization. We show that the estimator enjoys strong statistical guarantees, yet is much more practical and…

## 6 Citations

### Fused density estimation: theory and methods

- Mathematics, Computer ScienceJournal of the Royal Statistical Society: Series B (Statistical Methodology)
- 2019

A method for non‐parametric density estimation on geometric networks that reduces the original variational formulation to transform it into a tractable, finite dimensional quadratic program and compares the performance of various optimization techniques to solve the problem.

### A deconvolution path for mixtures

- Mathematics
- 2015

We propose a class of estimators for deconvolution in mixture models based on a simple two-step "bin-and-smooth" procedure applied to histogram counts. The method is both statistically and…

### An adaptive approach to non-parametric estimation of dynamic probability density functions

- Computer Science2016 13th Workshop on Positioning, Navigation and Communications (WPNC)
- 2016

An adaptive version of the Histogram Trend Filtering (HTF) is proposed, which is a relatively new method used for non-parametric density estimation and can deal with estimating both stationary and non-stationary distributions.

### A deconvolution path for mixtures

- Mathematics
- 2018

: We propose a class of estimators for deconvolution in mixture models based on a simple two-step “bin-and-smooth” procedure applied to histogram counts. The method is both statistically and…

### Multivariate Trend Filtering for Lattice Data

- MathematicsArXiv
- 2021

A multivariate version of trend filtering, called Kronecker trend filtering or KTF, for the case in which the design points form a lattice in d dimensions is studied, revealing a number of interesting phenomena, including the dominance of KTF over linear smoothers in estimating heterogeneously smooth functions.

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