The current thesis is structured in four parts. Vector smoothing methods are used to study environmental data, in particular records of extreme precipitation, the models utilized belong to the vector generalized additive class. In the statistical analysis of observational studies the identification and adjustment for prognostic factors is an important component of the analysis; employing flexible statistical methods to identify and characterize the effect of potential prognostic factors in a clinical trial, namely "generalized additive models", presents an alternative to the traditional linear statistical model. The classes of models for which the methodology gives generalized additive extensions include grouped survival data from the Surveillance, Epidemiology, and End Results tumors of the brain and the central nervous system database; we are employing piecewise linear functions of the covariates to characterize the survival experienced by the population. Finally, both descriptive and analytical methods are utilized to study incidence rates and tumor sizes associated with the disease.