Significance test of fuzzy regression model

Articles in Press

Document Type : Original Paper

Authors

1 Faculty of Mathematical Sciences and Computer, Shahid Chamran University of Ahvaz, Ahvaz, Iran

2 Department of Statistics , Mathematical Sciences and Computer Faculty, Shahid Chamran University of Ahvaz, Ahvaz, , Iran

3 Department of Statistics, Faculty of Mathematical Sciences and Computer,, Shahid Chamran University of Ahvaz, Ahvaz 6135714463, Iran

Abstract

Statistical significance determines whether the relationship between two or more variables is caused by factors other than chance and randomness. Statistical hypothesis testing is a method by which statistical significance is determined. By introducing fuzzy regression, several approaches were presented to estimate parameters of such the models. Now, most researches have conducted on the estimation method and little attention has been paid to the properties of estimators,, confidence intervals and significance tests.

The main idea here is to investigate the significance of estimated parameters in an applied study with fuzzy-valued real data in the framework of fuzzy regression modeling using $m$-estimators. For this purpose, by accessing the water and sewage data source of Ahvaz city, the required variables were first introduced.

Since $m$-estimators use an algorithm based on reweighted method, we are looking to determine the weight of the users in terms of the consumption pattern, that is, the weight of high consumption users and low consumption users is determined. Now, the company can first identify and classify the consumption patterns of each user based on the determined weights, and then deal with the stepped pricing of each cubic meter of water for each user. This idea requires providing a significant model of fuzzy regression. Since $m$-estimators of fuzzy regression model do not have a closed form, bootstrap is used to present the numerical indices of the estimators, confidence intervals and the significance test of the model. By analyzing the results and keeping significant parameters a suitable model was introduced.

Keywords

Main Subjects

Journal of Advanced Mathematical Modeling

Articles in Press, Accepted Manuscript
Available Online from 07 January 2025

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History

  • Receive Date: 30 June 2024
  • Revise Date: 25 November 2024
  • Accept Date: 07 January 2025

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