# A generic approach to nonparametric function estimation with mixed data

arXiv: https://arxiv.org/abs/1704.07457 · HTML: https://mlsanity.com/paper/1704.07457/

## Key facts

- Cited by 4 papers in the map (data through 14 Oct 2026).
- First posted on arXiv 24 Apr 2017.

## Built on by (most cited first, 4 of 4)

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- [Boosting with copula-based components](https://mlsanity.com/paper/2208.04669/) (2022)
- [Calibrating simplified vine copulas with a noise contrastive estimation approach](https://mlsanity.com/paper/2606.13213/) (2026)

## Abstract (arXiv)

In practice, data often contain discrete variables. But most of the popular nonparametric estimation methods have been developed in a purely continuous framework. A common trick among practitioners is to make discrete variables continuous by adding a small amount of noise. We show that this approach is justified if the noise distribution belongs to a certain class. In this case, any estimator developed in a purely continuous framework extends naturally to the mixed data setting. Estimators defined that way will be called continuous convolution estimators. They are extremely easy to implement and their asymptotic properties transfer directly from the continuous to the mixed data setting.