Most statistical methods assume homogeneous (outlier-free) data in which all data points satisfy the same model. However, real data are (not) NEVER homogeneous; and accurate identification of outliers plays an important role in statistical analysis.
Moreover, the OLS classic regression needs to satisfy many assumptions (normality, homoscedasticity of the residuals, linearity of the regression function...).
And with the OLS regression, we have as well to take care of the (multi)colinearity problem between the explanatory variables (measured by the Variance inflation factor (VIF)).
My 2 questions are the following :
1) When we realize the nonparametric MARS (Multivariate adaptive regression splines) regression, do we have to care about the outliers problem, about the (multi)colinearity problem ? And do we have to care about the different assumptions (normality, homoscedasticity of the residuals and linearity of the regression function...) like for OLS regression ? Or when we practice the MARS regression, we don't have to care about all these ?
2) If there are some, what are the conditions of application of MARS ? I have read that there must be lots of observations ? For example, if I have a sample size of n=33 countries and 1 dependent variable and 3 explanatory variables, is it enough for MARS regression ?
Best Regards, looking forward to reading You.