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Specific Gaussian mixtures are considered to solve simultaneously variable selection and clustering problems. A non asymptotic penalized criterion is proposed to choose the number of mixture components and the relevant variable subset. Because of the non linearity of the associated Kullback-Leibler contrast on Gaussian mixtures, a general model selection theorem for maximum likelihood estimation proposed by [Massart Concentration inequalities and model selection Springer, Berlin (2007). Lectures...
Specific Gaussian mixtures are considered to solve simultaneously
variable selection and clustering problems. A non asymptotic
penalized criterion is proposed to choose the number of mixture
components and the relevant variable subset. Because of the non
linearity of the associated Kullback-Leibler contrast on Gaussian
mixtures, a general model selection theorem for maximum likelihood
estimation proposed by [Massart Concentration inequalities and model selection
Springer, Berlin (2007).
Lectures...
The author applies the test criterion of P. Rothety to the statistical analysis of the positive correclation of symmetric pairs of observations. In this particular case he arrives at some new results. His work ends with a general proof of the consistency of Rothery's test.
We investigate a relation about subadditivity of functions. Based on subadditivity of functions, we consider some conditions for continuous -norms to act as the weakest -norm -based addition. This work extends some results of Marková-Stupňanová [15], Mesiar [18].
The present article studies the
conditions under which the almost
everywhere convergence and the
convergence in measure coincide.
An application in the statistical
estimation theory is outlined as
well.
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