1,470 research outputs found
Extensions of the parametric families of divergences used in statistical inference
summary:We propose a simple method of construction of new families of %-divergences. This method called convex standardization is applicable to convex and concave functions twice continuously differentiable in a neighborhood of with nonzero second derivative at the point . Using this method we introduce several extensions of the LeCam, power, and Matusita divergences. The extended families are shown to connect smoothly these divergences with the Kullback divergence or they connect various pairs of these particular divergences themselves. We investigate also the metric properties of divergences from these extended families
A new test procedure of independence in copula models via chi-square-divergence
We introduce a new test procedure of independence in the framework of
parametric copulas with unknown marginals. The method is based essentially on
the dual representation of -divergence on signed finite measures. The
asymptotic properties of the proposed estimate and the test statistic are
studied under the null and alternative hypotheses, with simple and standard
limit distributions both when the parameter is an interior point or not.Comment: 23 pages (2 figures). Submitted to publicatio
The Minimum S-Divergence Estimator under Continuous Models: The Basu-Lindsay Approach
Robust inference based on the minimization of statistical divergences has
proved to be a useful alternative to the classical maximum likelihood based
techniques. Recently Ghosh et al. (2013) proposed a general class of divergence
measures for robust statistical inference, named the S-Divergence Family. Ghosh
(2014) discussed its asymptotic properties for the discrete model of densities.
In the present paper, we develop the asymptotic properties of the proposed
minimum S-Divergence estimators under continuous models. Here we use the
Basu-Lindsay approach (1994) of smoothing the model densities that, unlike
previous approaches, avoids much of the complications of the kernel bandwidth
selection. Illustrations are presented to support the performance of the
resulting estimators both in terms of efficiency and robustness through
extensive simulation studies and real data examples.Comment: Pre-Print, 34 page
On a family of test statistics for discretely observed diffusion processes
We consider parametric hypotheses testing for multidimensional ergodic
diffusion processes observed at discrete time. We propose a family of test
statistics, related to the so called -divergence measures. By taking into
account the quasi-likelihood approach developed for studying the stochastic
differential equations, it is proved that the tests in this family are all
asymptotically distribution free. In other words, our test statistics weakly
converge to the chi squared distribution. Furthermore, our test statistic is
compared with the quasi likelihood ratio test. In the case of contiguous
alternatives, it is also possible to study in detail the power function of the
tests.
Although all the tests in this family are asymptotically equivalent, we show
by Monte Carlo analysis that, in the small sample case, the performance of the
test strictly depends on the choice of the function . Furthermore, in
this framework, the simulations show that there are not uniformly most powerful
tests
On preferred point geometry in statistics
A brief synopsis of progress in differential geometry in statistics is followed by a note
of some points of tension in the developing relationship between these disciplines. The preferred
point nature of much of statistics is described and suggests the adoption of a corresponding
geometry which reduces these tensions. Applications of preferred point geometry in statistics are
then reviewed. These include extensions of statistical manifolds, a statistical interpretation of
duality in Amari’s expected geometry, and removal of the apparent incompatibility between
(Kullback-Leibler) divergence and geodesic distance. Equivalences between a number of new
expected preferred point geometries are established and a new characterisation of total flatness
shown. A preferred point geometry of influence analysis is briefly indicated. Technical details are
kept to a minimum throughout to improve accessibility
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