## Electronic Journal of Statistics

- Electron. J. Statist.
- Volume 8, Number 1 (2014), 1-40.

### Additive inverse regression models with convolution-type operators

Thimo Hildebrandt, Nicolai Bissantz, and Holger Dette

#### Abstract

In a recent paper Birke and Bissantz (2009) considered the problem of nonparametric estimation in inverse regression models with convolution-type operators. For multivariate predictors nonparametric methods suffer from the curse of dimensionality and we consider inverse regression models with the additional qualitative assumption of additivity. In these models several additive estimators are studied. In particular, we propose a new estimation method for observations on regular spaced grid and investigate estimators under the random design assumption which are applicable when observations are not available on a grid. Finally, we compare these estimators with the marginal integration and the non-additive estimator by means of a simulation study. It is demonstrated that the new method yields a substantial improvement of the currently available procedures.

#### Article information

**Source**

Electron. J. Statist., Volume 8, Number 1 (2014), 1-40.

**Dates**

First available in Project Euclid: 29 January 2014

**Permanent link to this document**

https://projecteuclid.org/euclid.ejs/1391006406

**Digital Object Identifier**

doi:10.1214/13-EJS874

**Mathematical Reviews number (MathSciNet)**

MR3161732

**Zentralblatt MATH identifier**

1348.62135

**Subjects**

Primary: 62G08: Nonparametric regression

Secondary: 62G15: Tolerance and confidence regions 62G20: Asymptotic properties

**Keywords**

Inverse regression additive models convolution-type operators

#### Citation

Hildebrandt, Thimo; Bissantz, Nicolai; Dette, Holger. Additive inverse regression models with convolution-type operators. Electron. J. Statist. 8 (2014), no. 1, 1--40. doi:10.1214/13-EJS874. https://projecteuclid.org/euclid.ejs/1391006406