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Activity Number: 347 - Nonparametric Hybrid Methods
Type: Contributed
Date/Time: Wednesday, August 5, 2020 : 10:00 AM to 2:00 PM
Sponsor: Section on Nonparametric Statistics
Abstract #313988
Title: Poisson Regression with Laplace Measurement Error
Author(s): Shengnan Chen* and Weixing Song
Companies: Kansas State University and Kansas State University
Keywords: Poisson linear regression; Laplace measurement error; Tweedie Formula
Abstract:

In this talk, we propose an estimation procedure for a class of Poisson linear regression models when the covariate is contaminated with Laplace measurement error. The estimation procedure is based upon the maximum likelihood procedure and a Tweedie-type formula for the conditional expectation of the latent variable given the observed surrogate from Shi and Song (2015). Two scenarios are considered: the distribution of the latent variable is known and unknown. When the distribution of the latent variable is known, the distribution of the surrogate variable is also known. Then the Tweedie-type formula can be directly applied to the likelihood function to obtain the estimate. When the distribution of the latent variable is unknown, the distribution of the observed surrogate is replaced by the Rosenblatt-Parzen kernel density estimator in the likelihood equation. Large sample properties of the proposed estimator under those two situations are discussed, and simulation study shows that the new estimators are more efficient than the existing estimation procedures.


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