Parametric versus Semi and Nonparametric Regression Models

Abstract

Three types of regression models researchers need to be familiar with and know the requirements of each: parametric, semiparametric and nonparametric regression models. The type of modeling used is based on how much information are available about the form of the relationship between response variable and explanatory variables, and the random error distribution. In this article, differences between models, common methods of estimation, robust estimation, and applications are introduced. The R code for all the graphs and analyses presented here, in this article, is available in the Appendix.

A data-driven optimization model for the workover rig scheduling problem: Case study in an oil company

“…In the GLM, the error variable 𝜖 follows a distribution of the exponential family, which includes the Normal, Poisson, Binomial, and Gamma distributions. Linear coefficients are estimated using the maximum likelihood estimation (MLE) method if the residuals are non-Normal or ordinary least squares (OLS) otherwise (Yuan and Yang, 2005;Yan and Su, 2009;Mahmoud, 2019). Several packages are available in the R programming language to estimate generalized linear models.…”

Interval-valued Data Analysis: A Review

“…Parametric regression models should be used when the relation between the dependent and independent variables is known. Nonparametric regression models should be used if the relation is unknown and nonlinear [36].…”

Data-Driven Joint Chance-Constrained Optimization for the Workover Rig Scheduling Problem

“…As mentioned earlier, in the GLM, the error variable follows a distribution of the exponential family, which includes the Normal, Poisson, Binomial, and Gamma distributions. The linear coefficients are estimated using the maximum likelihood estimation (MLE) method if the residuals are non-Normal or the ordinary least squares (OLS), if Normal(Yuan and Yang 2005, Yan and Su 2009, Mahmoud 2019). However, if there is a large number of dummy variables; as a result…”