# An alternative local polynomial estimator for the error-in-variables problem

## TL;DR

This paper introduces a new local polynomial estimator for error-in-variables regression problems that reduces bias and improves numerical stability, supported by theoretical analysis and empirical validation.

## Contribution

It proposes an alternative estimator that avoids kernel transformation, with rigorous asymptotic analysis, an efficient implementation, and demonstrated advantages over existing methods.

## Key findings

- The new estimator is less biased than existing methods.
- It is numerically more stable in simulations.
- The estimator performs well on real motorcycle crash data.

## Abstract

We consider the problem of estimating a regression function when a covariate is measured with error. Using the local polynomial estimator of Delaigle, Fan, and Carroll (2009) as a benchmark, we propose an alternative way of solving the problem without transforming the kernel function. The asymptotic properties of the alternative estimator are rigorously studied. A detailed implementing algorithm and a computationally efficient bandwidth selection procedure are also provided. The proposed estimator is compared with the existing local polynomial estimator via extensive simulations and an application to the motorcycle crash data. The results show that the new estimator can be less biased than the existing estimator and is numerically more stable.