Univariate Exploratory Data Analysis
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The goal of this chapter is to present basic tools of univariate data analysis. We take a statistical approach firmly grounded in the calculus of probability. In particular, our interpretation of the data given by a set of observations is to view them as realizations of random objects with the same distribution. In the simplest case, these objects will be real numbers. The analysis of multivariate samples (i.e. observations of finite dimensional vectors with real components) is postponed to the next chapter. In fact, the title of this two-chapter set could as well have been “Distribution Modeling and Estimation”. Our emphasis is on the implementation of methods of data analysis, more than on the mathematical underpinnings of these methods. In other words, even though we introduce clear mathematical notation and terminology, we spend more time discussing practical examples than discussing mathematical results. After reviewing standard tools such as histograms, we consider the kernel density estimation method. We also emphasize the importance of quantiles plots, and of random simulations. Data used by financial institutions serve as illustrations of the power, as well as the limitations, of standard nonparametric estimation methods. Thus, when it comes to analyzing heavy-tailed distributions, we introduce semi-parametric estimation tools based on the theory of extreme value distributions.
KeywordsExponential Distribution Kernel Density Kernel Density Estimation Exploratory Data Analysis Quantile Function
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