49 research outputs found
New Entropy Estimator with an Application to Test of Normality
In the present paper we propose a new estimator of entropy based on smooth
estimators of quantile density. The consistency and asymptotic distribution of
the proposed estimates are obtained. As a consequence, a new test of normality
is proposed. A small power comparison is provided. A simulation study for the
comparison, in terms of mean squared error, of all estimators under study is
performed
On Empirical Likelihood in Semiparametric Two-Sample Density Ratio Models
We consider estimation and test problems for some semiparametric two-sample density ratio models. The profile empirical likelihood (EL) poses an irregularity problem under the null hypothesis that the laws of the two samples are equal. We show that a “dual” form of the profile EL is well defined even under the null hypothesis. A statistical test, based on the dual form of the EL ratio statistic (ELRS), is then proposed. We give an interpretation for the dual form of the ELRS through φ-divergences and “duality” technique. The asymptotic properties of the test statistic are presented both under the null and the alternative hypotheses, and an approximation to the power function is deduced
Parametric estimation and tests through divergences and duality technique
We introduce estimation and test procedures through divergence optimization
for discrete or continuous parametric models. This approach is based on a new
dual representation for divergences. We treat point estimation and tests for
simple and composite hypotheses, extending maximum likelihood technique. An
other view at the maximum likelihood approach, for estimation and test, is
given. We prove existence and consistency of the proposed estimates. The limit
laws of the estimates and test statistics (including the generalized likelihood
ratio one) are given both under the null and the alternative hypotheses, and
approximation of the power functions is deduced. A new procedure of
construction of confidence regions, when the parameter may be a boundary value
of the parameter space, is proposed. Also, a solution to the irregularity
problem of the generalized likelihood ratio test pertaining to the number of
components in a mixture is given, and a new test is proposed, based on -divergence on signed finite measures and duality technique