View Submission - COMPSTAT2022

A0622
**Title: **An approximation of the corrected naive estimator for a Poisson regression model with a measurement error
**Authors: **Kentarou Wada - Tokyo University of Science (Japan) **[presenting]**

Takeshi Kurosawa - Tokyo University of Science (Japan)

**Abstract: **The corrected naive estimator is proposed as a consistent estimator for a Poisson regression model with a measurement error. The corrected naive estimator is given by the solution of a system of equations such as the moment method. The corrected naive estimator requires a tedious calculation to obtain the explicit form. Moreover, the corrected naive estimator does not always have an explicit expression under the condition that the explanatory variable and measurement error are general distributions. In this situation, we can compute the corrected naive estimator numerically even if the corrected naive estimator does not have an explicit solution. It takes some computational costs to obtain the numerical solution of the corrected naive estimator. We propose the approximate corrected naive estimator. The approximate corrected naive estimator has a simple closed form, which does not require a troublesome calculation. The approximate corrected naive estimator can be applied for the condition that the corrected naive estimator does not have an explicit expression. Furthermore, the bias of the approximate corrected naive estimator has a close value to that of the corrected naive estimator.

Takeshi Kurosawa - Tokyo University of Science (Japan)