# Nonparametric estimation of copulas and copula densities by orthogonal projections

arXiv: https://arxiv.org/abs/2010.15351 · HTML: https://mlsanity.com/paper/2010.15351/

## Key facts

- Cited by 3 papers in the map (data through 14 Oct 2026).
- First posted on arXiv 29 Oct 2020.

## Built on by (most cited first, 3 of 3)

- [ROME: Robust Multi-Modal Density Estimator](https://mlsanity.com/paper/2401.10566/) (2024)
- [Non-parametric Clustering of Multivariate Populations with Arbitrary Sizes](https://mlsanity.com/paper/2211.06338/) (2022)
- [2-Cats: 2D Copula Approximating Transforms](https://mlsanity.com/paper/2309.16391/) (2023)

## Abstract (arXiv)

In this paper we study nonparametric estimators of copulas and copula densities. We first focus our study on a density copula estimator based on a polynomial orthogonal projection of the joint density. A new copula estimator is then deduced. Its asymptotic properties are studied: we provide a large functional class for which this construction is optimal in the minimax and maxiset sense and we propose a method selection for the smoothing parameter. An intensive simulation study shows the very good performance of both copulas and copula densities estimators which we compare to a large panel of competitors. A real dataset in actuarial science illustrates this approach.