ABSTRACT
An important component of statistical modeling is the quantification of the amount of discrepancy between data and the model through an appropriate divergence. Based on a sample of n independent and identically distributed observations, such divergences may be constructed, for example, between the empirical distribution function and its population version, or a nonparametric density estimate obtained from the data (constructed, if necessary, using an appropriate density estimation method such as the kernel density estimation) and the probability density function at the model. The first one represents a divergence between two distribution functions, while the second one is the divergence between two probability density functions. In this book, our primary attention will be on the density-based approach. A prominent example of the early use of the density-based idea is the chi-square distance of Pearson (1900).
