{"ID":2874812,"CreatedAt":"2026-06-01T04:54:23.091178241Z","UpdatedAt":"2026-06-01T04:54:23.091178241Z","DeletedAt":null,"paper_url":"https://arxiv.org/abs/2509.04709","arxiv_id":"2509.04709","title":"Strong Consistency of the SIMEX Estimator in Linear Regression with a Conditionally Poisson Covariate","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.","short_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 extrapolat...","url_abs":"https://arxiv.org/abs/2509.04709","url_pdf":"https://arxiv.org/pdf/2509.04709v1","authors":"[\"Aijun Yang\",\"Mary Lesperance\",\"Farouk S. Nathoo\"]","published":"2025-09-04T23:42:02Z","proceeding":"math.ST","tasks":"[\"math.ST\"]","methods":"[]","has_code":false}