March 2023 An extension of the partially linear Rice regression model for bimodal and correlated data
Julio C. S. Vasconcelos, Edwin M. M. Ortega, Roberto Vila, Vicente G. Cancho
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Braz. J. Probab. Stat. 37(1): 177-194 (March 2023). DOI: 10.1214/23-BJPS566


In this paper, we propose a new regression model based on an extension of the Rice distribution to model linear and nonlinear effects for correlated data in the presence of bimodality. The new model is referred to as the odd log-logistic Rice distribution and we provide general mathematical properties, including the event risk and moments. We discuss parameter estimation by the penalized maximum likelihood method. We also present several simulations with different parameter configurations and sample sizes to analyze the behavior of the maximum likelihood estimators, as well as to study the empirical distribution of the quantile residuals. The usefulness of the proposed regression model is proved empirically through analysis of a real dataset.

Funding Statement

The authors were supported by CNPq, CAPES and FAP-DF, Brazil.


The authors would like to thank the anonymous referees, an Associate Editor and the Editor for their constructive comments that improved the quality of this paper.


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Julio C. S. Vasconcelos. Edwin M. M. Ortega. Roberto Vila. Vicente G. Cancho. "An extension of the partially linear Rice regression model for bimodal and correlated data." Braz. J. Probab. Stat. 37 (1) 177 - 194, March 2023.


Received: 1 January 2022; Accepted: 1 February 2023; Published: March 2023
First available in Project Euclid: 27 April 2023

MathSciNet: MR4580890
zbMATH: 07692855
Digital Object Identifier: 10.1214/23-BJPS566

Keywords: partially linear regression , p-splines , residual analysis , simulation study

Rights: Copyright © 2023 Brazilian Statistical Association


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Vol.37 • No. 1 • March 2023
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