On wavelet to select the parametric form of a regression model

We consider the problem of estimating the relationship between a response variable and a set of explanatory variates. We suppose a set of parametric forms as candidates for the aforementioned regression. Wavelet regression is used as auxiliary for the choice of the most appropriate parametric form of the model, particularly for the cases of nonlinear and generalized linear models. The use of a wavelet method for the choice of the most appropriate parametric relationship is interesting in practice for four main reasons. The first is that it provides a statistically sound method to choose the 'best' parametric model for a data set, given that no pre-determined regression form nor probability distribution are assumed to be known. On the other hand, the parametric models are easier to interpret and more convenient for prediction purposes than non-parametric ones. Moreover, since wavelet methods possess a natural data-driven shrinkage paradigm, we can ascertain that overfitting is not expected. For instance, the results show that few non-null coefficients remain after thresholding. Finally, fast wavelet methods are widely available which makes this a feasible procedure for researchers as well as data analysts. We evaluate the performance of the proposed wavelet procedure based on the correct classification rates of the underlying parametric form on a range of candidate models, taking into account a wide range of scenarios. The method is also illustrated by real data analyses. Computer codes are available asCONSELHO NACIONAL DE DESENVOLVIMENTO CIENTÍFICO E TECNOLÓGICO - CNPQFUNDAÇÃO DE AMPARO À PESQUISA DO ESTADO DE SÃO PAULO - FAPESP309230/2017-92018/04654-