# 05/03/2021 - Wavelets and their use to solve statistical problem - Speaker: Michel Montoril (UFSCar)

**UFSCar/USP joint Seminar**

**Schudele:**

05/03/2021 to 14h

**Localization:**Google Meet - Presentation link (up to one hour before the lecture at www.pipges.ufscar.br)

**Título (title):**

Wavelets and their use to solve statistical problem

**Speaker****:**Michel Montoril (UFSCar)

**Abstract:**In this talk we introduce basic concepts related to wavelet bases and their use in Statistics. We briefly overview the construction and the importance of wavelets in the analysis of functions of interest. The application of wavelets to solve statistical problems is illustrated with some examples, namely: probability density function estimation of biased data, classification and additive regression. We also emphasize the estimation of the probability function in mixture regression models. Basically, there is a process Y that can be (randomly) observed along the time, say T, which is supported on the unit interval. For a fixed time T = t, the process can be either a random variable (r.v.) V, with probability f(t), or a r.v. W, with probability 1 - f(t), where V and W are assumed to have known and different means. This method will be illustrated by simulation studies and a real data set application.