Research ArticleOpen accessIn the keywordsLossy Asymptotic Equipartition Property for Networked Data StructuresKwabena Doku-AmponsahIn this study, we prove a Generalized Information Theory for Networked Data Structures modelled as random graphs. The main tools in this study remain large deviation principles for properly defined empirical measures on random graphs. To motivate the paper, we apply our main result to a concrete example from the field of Biology. …Journal of Mathematics and Statistics, Vol. 13, Issue 2 · 24 May 2017 · 6,979 accessesView PDFCite
Research ArticleOpen accessIn the keywordsAsymptotic Properties of Local Sampling on ManifoldYury Aleksandrovich YanovichIn many applications, the real high-dimensional data occupy only a very small part in the high dimensional ‘observation space’ whose intrinsic dimension is small. The most popular model of such data is Manifold model which assumes that the data lie on or near an unknown manifold Data Manifold, (DM) of lower dimensionality embedded in an ambient high-dimensional input space (Manifold … …Journal of Mathematics and Statistics, Vol. 12, Issue 3 · 26 Aug 2016 · 7,698 accessesView PDFCite
Research ArticleOpen accessIn the abstractAbsolute Measures of Interindividual Variation: A Simulation StudyJosé Moral-de la RubiaFour absolute measures and one relative measure of interindividual variability have been defined, together with their point and interval estimation (bootstrap and asymptotic), and an R script has been developed for their computation. However, further simulation studies are required to strengthen their methodological evaluation. This study focused on the three absolute measures with potentially better regularity conditions, Mean Interindividual Differences … …Journal of Mathematics and Statistics, Vol. 22, Issue 1 · 4 Aug 2026 · 957 accessesView PDFCite
Research ArticleOpen accessAll words, across the recordTHE RATE FUNCTION OF S-MIXING PROCESS AND ITS APPLICATION IN EVALUATING EMPIRICAL LIKELIHOOD TESTSXing WangIn this study we show that the rate function of S-Mixing stationary process with part of the hypermixing condition is equivalent to the Kullback-Leibler distance. This finding can be used to extend the result of the optimality of empirical likelihood test in i.i.d setting to weakly depended case, so that the Asymptotic Relative Efficiency (ARE) of the empirical likelihood test … …Journal of Mathematics and Statistics, Vol. 9, Issue 4 · 28 Oct 2013 · 6,615 accessesView PDFCite