  Recently in [1, 2], Ali-Akbar Bromideh introduced the Kullback-Leibler
Divergence (KLD) test statistic in discrim- inating between two models. It was
found that the Ratio Minimized Kulback-Leibler Divergence (RMKLD) works better
than the Ratio of Maximized Likelihood (RML) for small sample size. The aim of
this paper is to generalize the works of Ali-Akbar Bromideh by proposing a
hypothesis testing based on Bregman divergence in order to improve the process
of choice of the model. Our aproach differs from him. After observing n data
points of unknown density f ; we firstly measure the closness between the bias
reduced kernel density estimator and the first estimated candidate model.
Secondly between the bias reduced kernel density estimator and the second
estimated candidate model. In these two cases Bregman Divergence (BD) and the
bias reduced kernel estimator [3] focuses on improving the con- vergence rates
of kernel density estimators are used. Our testing procedure for model
selection is thus based on the comparison of the value of model selection test
statistic to critical values from a standard normal table. We establish the
asymptotic properties of Bregman divergence estimator and approximations of the
power functions are deduced. The multi-step MLE process will be used to
estimate the parameters of the models. We explain the applicability of the BD
by a real data set and by the data generating process (DGP). The Monte Carlo
simulation and then the numerical analysis will be used to interpret the
result.
