Tail orderings and the total time on test transform
The paper presents some connections between two tail orderings of distributions and the total time on test transform. The procedure for testing the pure-tail ordering is proposed.
The 123 theorem of Probability Theory and Copositive Matrices
Alon and Yuster give for independent identically distributed real or vector valued random variables X, Y combinatorially proved estimates of the form Prob(∥X − Y∥ ≤ b) ≤ c Prob(∥X − Y∥ ≤ a). We derive these using copositive matrices instead. By the same method we also give estimates for the real valued case, involving X + Y and X − Y, due to Siegmund-Schultze and von Weizsäcker as generalized by Dong, Li and Li. Furthermore, we formulate a version of the above inequalities as an integral inequality...
The best constant in the Khintchine inequality for complex Steinhaus variables, the case p=1
The best estimation of a ratio inequality for continuous martingales
The best possibility of the bound for the Kantorovich inequality and some remarks.
The convergence of sums of transition probabilities of a positive recurrent Markov chain.
The Doob inequality and strong law of large numbers for multidimensional arrays in general Banach spaces
We establish the Doob inequality for martingale difference arrays and provide a sufficient condition so that the strong law of large numbers would hold for an arbitrary array of random elements without imposing any geometric condition on the Banach space. Some corollaries are derived from the main results, they are more general than some well-known ones.
The Kolmogorov distance between the binomial and Poisson laws: efficient algorithms and sharp estimates.
The large deviation principle for certain series
We study the large deviation principle for stochastic processes of the form , where is a sequence of i.i.d.r.v.'s with mean zero and . We present necessary and sufficient conditions for the large deviation principle for these stochastic processes in several situations. Our approach is based in showing the large deviation principle of the finite dimensional distributions and an exponential asymptotic equicontinuity condition. In order to get the exponential asymptotic equicontinuity condition,...
The large deviation principle for certain series
We study the large deviation principle for stochastic processes of the form , where is a sequence of i.i.d.r.v.’s with mean zero and . We present necessary and sufficient conditions for the large deviation principle for these stochastic processes in several situations. Our approach is based in showing the large deviation principle of the finite dimensional distributions and an exponential asymptotic equicontinuity condition. In order to get the exponential asymptotic equicontinuity condition,...
The mean of a maximum likelihood estimator associated with the Brownian bridge.
The missing factor in Hoeffding's inequalities
The notion of -weak dependence and its applications to bootstrapping time series.
The proportional likelihood ratio order and applications.
In this paper, we introduce a new stochastic order between continuous non-negative random variables called the PLR (proportional likelihood ratio) order, which is closely related to the usual likelihood ratio order. The PLR order can be used to characterize random variables whose logarithms have log-concave (log-convex) densities. Many income random variables satisfy this property and they are said to have the IPLR (increasing proportional likelihood ratio) property (DPLR property). As an application,...
The Reverse Isoperimetric Problem for Gaussian Measure.
The strong law of large numbers for -statistics with dependent data.
The variogram and estimation error in connection with the assessment of continuous streams.
Theory of classification : a survey of some recent advances
The last few years have witnessed important new developments in the theory and practice of pattern classification. We intend to survey some of the main new ideas that have led to these recent results.
Theory of Classification: a Survey of Some Recent Advances
The last few years have witnessed important new developments in the theory and practice of pattern classification. We intend to survey some of the main new ideas that have led to these recent results.
Thin-shell concentration for convex measures
We prove that for s < 0, s-concave measures on ℝⁿ exhibit thin-shell concentration similar to the log-concave case. This leads to a Berry-Esseen type estimate for most of their one-dimensional marginal distributions. We also establish sharp reverse Hölder inequalities for s-concave measures.