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On some beta ridge regression estimators : method, simulation and application

Qasim, Muhammad LU ; Månsson, Kristofer and Golam Kibria, B. M. (2021) In Journal of Statistical Computation and Simulation 91(9). p.1699-1712
Abstract

The classic statistical method for modelling the rates and proportions is the beta regression model (BRM). The standard maximum likelihood estimator (MLE) is used to estimate the coefficients of the BRM. However, this MLE is very sensitive when the regressors are linearly correlated. Therefore, this study introduces a new beta ridge regression (BRR) estimator as a remedy to the problem of instability of the MLE. We study the mean squared error properties of the BRR estimator analytically and then based on the derived MSE, we suggest some new estimators of the shrinkage parameter. We also suggest a median squared error (SE) performance criterion, which can be used to achieve strong evidence in favour of the proposed method for the Monte... (More)

The classic statistical method for modelling the rates and proportions is the beta regression model (BRM). The standard maximum likelihood estimator (MLE) is used to estimate the coefficients of the BRM. However, this MLE is very sensitive when the regressors are linearly correlated. Therefore, this study introduces a new beta ridge regression (BRR) estimator as a remedy to the problem of instability of the MLE. We study the mean squared error properties of the BRR estimator analytically and then based on the derived MSE, we suggest some new estimators of the shrinkage parameter. We also suggest a median squared error (SE) performance criterion, which can be used to achieve strong evidence in favour of the proposed method for the Monte Carlo simulation study. The performance of BRR and MLE is appraised through Monte Carlo simulation. Finally, an empirical application is used to show the advantages of the proposed estimator.

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author
; and
publishing date
type
Contribution to journal
publication status
published
subject
keywords
Beta regression model, mean Squared error, median Squared error, multicollinearity, simulation study
in
Journal of Statistical Computation and Simulation
volume
91
issue
9
pages
14 pages
publisher
Taylor & Francis
external identifiers
  • scopus:85099436227
ISSN
0094-9655
DOI
10.1080/00949655.2020.1867549
language
English
LU publication?
no
additional info
Publisher Copyright: © 2021 The Author(s). Published by Informa UK Limited, trading as Taylor & Francis Group.
id
dfb8da43-8dc5-4b2d-8252-bf996fc429eb
date added to LUP
2025-04-01 09:28:03
date last changed
2025-04-04 15:04:47
@article{dfb8da43-8dc5-4b2d-8252-bf996fc429eb,
  abstract     = {{<p>The classic statistical method for modelling the rates and proportions is the beta regression model (BRM). The standard maximum likelihood estimator (MLE) is used to estimate the coefficients of the BRM. However, this MLE is very sensitive when the regressors are linearly correlated. Therefore, this study introduces a new beta ridge regression (BRR) estimator as a remedy to the problem of instability of the MLE. We study the mean squared error properties of the BRR estimator analytically and then based on the derived MSE, we suggest some new estimators of the shrinkage parameter. We also suggest a median squared error (SE) performance criterion, which can be used to achieve strong evidence in favour of the proposed method for the Monte Carlo simulation study. The performance of BRR and MLE is appraised through Monte Carlo simulation. Finally, an empirical application is used to show the advantages of the proposed estimator.</p>}},
  author       = {{Qasim, Muhammad and Månsson, Kristofer and Golam Kibria, B. M.}},
  issn         = {{0094-9655}},
  keywords     = {{Beta regression model; mean Squared error; median Squared error; multicollinearity; simulation study}},
  language     = {{eng}},
  month        = {{01}},
  number       = {{9}},
  pages        = {{1699--1712}},
  publisher    = {{Taylor & Francis}},
  series       = {{Journal of Statistical Computation and Simulation}},
  title        = {{On some beta ridge regression estimators : method, simulation and application}},
  url          = {{http://dx.doi.org/10.1080/00949655.2020.1867549}},
  doi          = {{10.1080/00949655.2020.1867549}},
  volume       = {{91}},
  year         = {{2021}},
}