  This paper deals with four types of point estimators based on minimization of
information-theoretic divergences between hypothetical and empirical
distributions. These were introduced (i) by Liese & Vajda (2006) and
independently Broniatowski & Keziou (2006), called here power superdivergence
estimators, (ii) by Broniatowski & Keziou (2009), called here power
subdivergence estimators, (iii) by Basu et al. (1998), called here power
pseudodistance estimators, and (iv) by Vajda (2008) called here Renyi
pseudodistance estimators. The paper studies and compares general properties of
these estimators such as consistency and influence curves, and illustrates
these properties by detailed analysis of the applications to the estimation of
normal location and scale.
