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Statistical modeling via wavelets


One of the main interests in Statistics is the satisfactory modeling of data sets in several different situations and contexts. Due to the computational advances in last years, the use of non-parametric approaches have gained more and more attention of researchers, specially because of the ability of these methods in proposing and/or validating other existing approaches. Besides, it is important to mention the flexibility of non-parametric models, where they are capable of adapting to specific features of the data. A non-parametric tool that has gained importance are wavelet bases. The main reason is their ability of estimating functions with good quality, where they can capture irregularities of functions better than other methods, such as Fourier series. In this project we intend to model data sets using wavelet bases. The main goal is the proposal of new methodologies to estimate discriminant functions for high dimensional data, such as functional data, and the estimation of probability density functions of size-biased data. (AU)

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