• Corpus ID: 248693626

The na\"ive estimator of a Poisson regression model with measurement errors

@inproceedings{Wada2022TheNE,
  title={The na\"ive estimator of a Poisson regression model with measurement errors},
  author={Kentarou Wada and Takeshi Kurosawa},
  year={2022}
}

• Kentarou Wada, T. Kurosawa
• Published 11 May 2022
• Mathematics

We generalize the na¨ıve estimator of a Poisson regression model with measurement errors as discussed in Kukush et al. [1]. The explanatory variable is not always normally distributed as they assume. In this study, we assume that the explanatory variable and measurement error are not limited to a normal distribution. We clarify the requirements for the existence of the na¨ıve estimator and derive its asymptotic bias and asymptotic mean squared error (MSE). In addition, we propose a consistent estimator of the true parameter by correcting the bias of the na¨ıve estimator. As illustrative examples, we present simulation studies that compare the performance of the na¨ıve estimator and new estimator for a Gamma explanatory variable with a normal error or a Gamma error.