New contributions to the identifications of groups in nonparametric curves

Resumo

Several problems in statistical inference can be considered as part of statistical modelling. The way to aboard inference problems leads to two different focus: parametric and nonparametric ones. Parametric models require assumptions about structure and distributional form, unlike nonparametric models in which the model structure is not specified in advance but is instead determined from data. As nonparametric models are flexible, their applicability has gained increasing importance in widely diverse fields, such as medicine, biology end engineering and their development continue at an active pace today. One of the main goals in nonparametric statistical modelling is to understand the dependence between a response variable and an explanatory variable through regression models. The comparison of these regression models has been widely investigated in the literature. This problem has also been abroad in many longitudinal medical studies in which is interesting to compare survival between patients. However, when the null hypothesis of equality of curves is rejected, ascertaining whether groups of curves can exist is still a challenge. Thus, the main objective of this dissertation is to determine groups of multiple survival curves and regression curves. Regarding this, a new procedure is presented. Its performance is analysed through simulation studies and it is proved that is able to assign curves to their corresponding groups and to select the optimal number of them. Additionally, the method is illustrated using different real data applications. Finally, with the aim of making these methods available for their usage in real-life problems by researchers, developers or stakeholders, an R package (clustcurv v2.0.1) has been developed which is freely available from the CRAN (Comprehensive R Archive Network).