Strong Consistency of the SIMEX Estimator in Linear Regression with a Conditionally Poisson Covariate

2025/09/04 by Aijun Yang, Yang, Aijun, Mary Lesperance +3 · 1 citation
Mathematics · #FOS: Mathematics #Statistical Methods and Inference #Statistics Theory (math.ST)

paper · pdf · doi:10.48550/arxiv.2509.04709

openalex publication_date 2025/09/04 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

This paper considers estimation for linear regression analysis with covariate measurement error arising from Poisson surrogates. We consider cases where covariates follow a conditional Poisson distribution, capturing non-Gaussian and heteroscedastic error structures. To address this, we extend the simulation extrapolation (SIMEX) algorithm to the conditional Poisson setting (POI-SIMEX), enabling robust adjustment in the absence of internal validation data. Theoretical analysis establishes strong consistency of the POI-SIMEX estimator under a linear regression framework.

Citations

• Simulation-Selection-Extrapolation: Estimation in High-Dimensional\n Errors-in-Variables Models
• SIMEX estimation for single-index model with covariate measurement error

Cited by

• Survival Analysis with Discrete Biomarkers Under a Semiparametric Bayesian Conditional Poisson Model

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• Simulation-Selection-Extrapolation: Estimation in High-Dimensional\n Errors-in-Variables Models