Parametric and partially linear regressions for agricultural economy data

Abstract

We propose two new regressions, one parametric and other partially linear based on an extended Birnbaum–Saunders distribution. This distribution includes, as special cases, the exponentiated Birnbaum–Saunders, odd log-logistic Birnbaum–Saunders and Birnbaum–Saunders distributions. Several mathematical properties are presented. We adopt the maximum likelihood method to estimate the parameters of the parametric regression model and the penalized maximum likelihood method to estimate the parameters of the partially linear regression model. We study the behavior of the estimators through Monte Carlo simulations considering different scenarios and also extended the quantile residuals for the new regression models to verify the versatility of the parametric regression model. An analysis is carried out using average price data (R$) received by producers and wholesalers collected by Hortifruti/Cepea-Esalq/USP (Brazil). Similarly, the flexibility of the partially linear regression model is proved through an analysis with data on the average price of a hectare of rural property with improvements in the city of Itapeva-SP, Brazil. These applications empirically show that the proposed regression models have a better quality of fit than other existing regression models in the literature.

Keywords:

• Bimodal data
• mathematical properties
• nonlinear effects
• penalized smoothing
• regression model

Notes

1 http://mathworld.wolfram.com/InverseErf.html

Additional information

Funding

This work was supported by Cepea/Esalq-USP, IEA, CATI, CNPq and CAPES, Brazil.