Regressão Wavelet aplicada ao modelo de regressão normal não linear

Abstract

Nonlinear regression methods represent a relevant research field due your practical applicability in other áreas of knowledge. However, defining a nonlinear function, which best defines the data, is not an easy task when the mathematical relationship between the response variable and the independent variables is unksnown. Regarding the taste of how to find the best nonlinear function for a regression model, the aim of this work is to evaluate the performance of the Wavelet Regression Model (WM) in the detection of a true nonlinear function. Thus, four nonlinear functions, were selected from a total of 25 used in this work. Then, a Monte Carlo simulation study was performed, taking into account 1000 replicates, 36 different scenarios, four true nonlinear functions, three sample size and degrees of relationship between X and Y. We avaluate the true classification rate of the WM. We identify, in the scenarios where the sample size is larger and/or the relation between X and Y is moderate. However the WM presented a bad performance for small samples (n = 128), increasing the true classification rate when the sample size incrase. In general, there is evidence that the Wavelet Regression Model presented a good performance to detected the true nonlinear functions, specially for the Root Mean Square Error (RMSE) measure. There fore, based on these results we conclude that the WM is an important tool to identify the true nonlinear regression function when it is unknown.