Simultaneous inference for Berkson errors-in-variables regression under fixed design

TL;DR

This paper develops a nonparametric inference method for Berkson errors-in-variables regression with fixed design, providing finite-sample confidence bands and demonstrating their effectiveness through simulations.

Contribution

It introduces a new estimator accounting for predictor errors in a fixed design setting and derives finite-sample uniform confidence bands using Gaussian approximation techniques.

Findings

Finite sample bounds on coverage error of confidence bands

Use of Gaussian anti-concentration for confidence interval construction

Simulation results show good performance of the proposed method

Abstract

In various applications of regression analysis, in addition to errors in the dependent observations also errors in the predictor variables play a substantial role and need to be incorporated in the statistical modeling process. In this paper we consider a nonparametric measurement error model of Berkson type with fixed design regressors and centered random errors, which is in contrast to much existing work in which the predictors are taken as random observations with random noise. Based on an estimator that takes the error in the predictor into account and on a suitable Gaussian approximation, we derive %uniform confidence statements for the function of interest. In particular, we provide finite sample bounds on the coverage error of uniform confidence bands, where we circumvent the use of extreme-value theory and rather rely on recent results on anti-concentration of Gaussian processes. In a simulation study we investigate the performance of the uniform confidence sets for finite samples.