Uncertain maximum likelihood estimation for uncertain Von Bertalanffy regression model with real-life data

Abstract

Regression analysis is a potent tool to explore the relationship of variables and widely used in many areas. Classical statistics assume that the residual of regression model should follow the Gauss-Markov hypothesis. However, in many cases, the data is not obeying this hypothesis particularly real-life data. Therefore, this paper explores the Von Bertalanffy regression model under the framework of the uncertainty theory, and employs the uncertain maximum likelihood estimation (MLE) to estimate the unknown parameters. Furthermore, the uncertain hypothesis test and an algorithm for data modification which aimed to find outliers and modify data are studied, then the forecast value and confidence interval be formulated. Finally, a real-life numerical example of applying the above theories be given, this example shows that the uncertain MLE has better performance compare with the uncertain least squares and the least absolute deviations methods. Consequently, the uncertain MLE is a better way to deal with the real-life data.