  The aim of this paper is to introduce new statistical criterions for
estimation, suitable for inference in models with common continuous support.
This proposal is in the direct line of a renewed interest for divergence based
inference tools imbedding the most classical ones, such as maximum likelihood,
Chi-square or Kullback Leibler. General pseudodistances with decomposable
structure are considered, they allowing to define minimum pseudodistance
estimators, without using nonparametric density estimators. A special class of
pseudodistances indexed by {\alpha}>0, leading for {\alpha}\downarrow0 to the
Kulback Leibler divergence, is presented in detail. Corresponding estimation
criteria are developed and asymptotic properties are studied. The estimation
method is then extended to regression models. Finally, some examples based on
Monte Carlo simulations are discussed.
