The power divergence and the density power divergence families: the mathematical connection

The power divergence family of Cressie and Read (1984) is a highly popular family of density-based divergences which is widely used in robust parametric estimation and multinomial goodness-of-fit testing. This family forms a subclass of the family of φ-divergences (Csiszár, 1963; Pardo, 2006) or disparities (Lindsay, 1994). The more recently described family of density power divergences (Basu et al., 1998) is also extremely useful in robust parametric estimation. This paper explores the mathematical connection between these two families and establishes some interesting links. AMS (2000) subject classification. Primary 62F10, 62F35; Secondary 62-07.