Additive inverse regression models with convolution-type operators

TL;DR

This paper introduces additive inverse regression models with convolution operators, demonstrating through simulations that the new estimators outperform existing methods, especially in multivariate settings with non-grid data.

Contribution

The paper develops and compares additive estimators for inverse regression models with convolution operators, improving estimation accuracy in multivariate, non-grid data scenarios.

Findings

New additive estimators outperform existing methods

Simulation shows substantial improvement in estimation accuracy

Applicable to non-grid, multivariate data

Abstract

In a recent paper Birke and Bissantz (2008) 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 investigate estimators under the random design assumption which are applicable when observations are not available on a grid. Finally, we compare this estimator 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.