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A new Poisson Liu Regression Estimator : method and application

Qasim, Muhammad LU ; Kibria, B. M.G. ; Månsson, Kristofer and Sjölander, Pär (2020) In Journal of Applied Statistics 47(12). p.2258-2271
Abstract

This paper considers the estimation of parameters for the Poisson regression model in the presence of high, but imperfect multicollinearity. To mitigate this problem, we suggest using the Poisson Liu Regression Estimator (PLRE) and propose some new approaches to estimate this shrinkage parameter. The small sample statistical properties of these estimators are systematically scrutinized using Monte Carlo simulations. To evaluate the performance of these estimators, we assess the Mean Square Errors (MSE) and the Mean Absolute Percentage Errors (MAPE). The simulation results clearly illustrate the benefit of the methods of estimating these types of shrinkage parameters in finite samples. Finally, we illustrate the empirical relevance of... (More)

This paper considers the estimation of parameters for the Poisson regression model in the presence of high, but imperfect multicollinearity. To mitigate this problem, we suggest using the Poisson Liu Regression Estimator (PLRE) and propose some new approaches to estimate this shrinkage parameter. The small sample statistical properties of these estimators are systematically scrutinized using Monte Carlo simulations. To evaluate the performance of these estimators, we assess the Mean Square Errors (MSE) and the Mean Absolute Percentage Errors (MAPE). The simulation results clearly illustrate the benefit of the methods of estimating these types of shrinkage parameters in finite samples. Finally, we illustrate the empirical relevance of our newly proposed methods using an empirically relevant application. Thus, in summary, via simulations of empirically relevant parameter values, and by a standard empirical application, it is clearly demonstrated that our technique exhibits more precise estimators, compared to traditional techniques–at least when multicollinearity exist among the regressors.

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author
; ; and
publishing date
type
Contribution to journal
publication status
published
subject
keywords
Liu estimator, MLE, MSE, Poisson regression, shrinkage estimators, simulation study
in
Journal of Applied Statistics
volume
47
issue
12
pages
14 pages
publisher
Routledge
external identifiers
  • scopus:85077385521
ISSN
0266-4763
DOI
10.1080/02664763.2019.1707485
language
English
LU publication?
no
additional info
Publisher Copyright: © 2019 The Author(s). Published by Informa UK Limited, trading as Taylor & Francis Group.
id
4de1f063-45fc-4769-b3ab-e5f1e57b0ee3
date added to LUP
2025-04-01 09:28:44
date last changed
2025-04-04 14:52:56
@article{4de1f063-45fc-4769-b3ab-e5f1e57b0ee3,
  abstract     = {{<p>This paper considers the estimation of parameters for the Poisson regression model in the presence of high, but imperfect multicollinearity. To mitigate this problem, we suggest using the Poisson Liu Regression Estimator (PLRE) and propose some new approaches to estimate this shrinkage parameter. The small sample statistical properties of these estimators are systematically scrutinized using Monte Carlo simulations. To evaluate the performance of these estimators, we assess the Mean Square Errors (MSE) and the Mean Absolute Percentage Errors (MAPE). The simulation results clearly illustrate the benefit of the methods of estimating these types of shrinkage parameters in finite samples. Finally, we illustrate the empirical relevance of our newly proposed methods using an empirically relevant application. Thus, in summary, via simulations of empirically relevant parameter values, and by a standard empirical application, it is clearly demonstrated that our technique exhibits more precise estimators, compared to traditional techniques–at least when multicollinearity exist among the regressors.</p>}},
  author       = {{Qasim, Muhammad and Kibria, B. M.G. and Månsson, Kristofer and Sjölander, Pär}},
  issn         = {{0266-4763}},
  keywords     = {{Liu estimator; MLE; MSE; Poisson regression; shrinkage estimators; simulation study}},
  language     = {{eng}},
  month        = {{09}},
  number       = {{12}},
  pages        = {{2258--2271}},
  publisher    = {{Routledge}},
  series       = {{Journal of Applied Statistics}},
  title        = {{A new Poisson Liu Regression Estimator : method and application}},
  url          = {{http://dx.doi.org/10.1080/02664763.2019.1707485}},
  doi          = {{10.1080/02664763.2019.1707485}},
  volume       = {{47}},
  year         = {{2020}},
}