Related papers: Rosenthal's inequalities for independent and negat…
We establish a large deviation theorem for the empirical spectral distribution of random covariance matrices whose entries are independent random variables with mean 0, variance 1 and having controlled forth moments. Some new properties of…
In this paper, by using the representation theorem for sublinear expectations, we give a simple proof to obtain two inequalities about the sample mean for independent random vectors under sublinear expectations.
This article establishes novel strong uniform laws of large numbers for randomly weighted sums such as bootstrap means. By leveraging recent advances, these results extend previous work in their general applicability to a wide range of…
The probabilistic characterization of the relationship between two or more random variables calls for a notion of dependence. Dependence modeling leads to mathematical and statistical challenges, and recent developments in extremal…
Based on a law of the iterated logarithm for independent random variables sequences, an iterated logarithm theorem for NA sequences with non-identical distributions is obtained. The proof is based on a Kolmogrov-type exponential inequality.
For a sequence $\{X_{n}, \, n \geqslant 1 \}$ of nonnegative random variables where $\max[\min(X_{n} - s,t),0]$, $t > s \geqslant 0$, satisfy a moment inequality, sufficient conditions are given under which $\sum_{k=1}^n (X_k - \mathbb{E}…
In this paper we extend the Bernstein, Prohorov and Bennett inequalities to the noncommutative setting. In addition we provide an improved version of the noncommutative Rosenthal inequality, essentially due to Nagaev, Pinelis and Pinelis,…
It is well known that a random vector with given marginal distributions is comonotonic if and only if it has the largest sum with respect to the convex order [ Kaas, Dhaene, Vyncke, Goovaerts, Denuit (2002), A simple geometric proof that…
This paper proposes new tests of conditional independence of two random variables given a single-index involving an unknown finite-dimensional parameter. The tests employ Rosenblatt transforms and are shown to be distribution-free while…
Positive dependencies have been compared in the literature under rather strong assumptions such as equality of conditional distributions, exchangeability, or stationarity. We establish supermodular ordering results for distributions that…
We analyse the proof of Bell's inequality and demonstrate that this inequality is related to one particular model of probability theory, namely Kolmogorov measure-theoretical axiomatics, 1933. We found a (numerical) statistical correction…
We develop the distribution of the number of hypotheses found to be statistically significant using the rule from Benjamini and Hochberg (1995) for controlling the false discovery rate (FDR). This distribution has both a small sample form…
We provide a test for the specification of a structural model without identifying assumptions. We show the equivalence of several natural formulations of correct specification, which we take as our null hypothesis. From a natural empirical…
We analyze the extreme value dependence of independent, not necessarily identically distributed multivariate regularly varying random vectors. More specifically, we propose estimators of the spectral measure locally at some time point and…
In this paper, we obtain general representations for the joint distributions and copulas of arbitrary dependent random variables absolutely continuous with respect to the product of given one-dimensional marginal distributions. The…
Let $X_1,X_2,...$ be a sequence of independent and identically distributed random variables, and put $S_n=X_1+...+X_n$. Under some conditions on the positive sequence $\tau_n$ and the positive increasing sequence $a_n$, we give necessary…
The Rotar central limit theorem is a remarkable theorem in the non-classical version since it does not use the condition of asymptotic infinitesimality for the independent individual summands, unlike the theorems named Lindeberg's and…
We establish noncommutative analogs of some well-known large deviation inequalities for noncommutative random variables. Firstly, for the noncommutative independent case, we characterize the uniformly exponential integrability of random…
The law of large numbers (LLN) and central limit theorem (CLT) are long and widely been known as two fundamental results in probability theory. Recently problems of model uncertainties in statistics, measures of risk and superhedging in…
We perform frequency analysis of the EPR-Bell argumentation. One of the main consequences of our investigation is that the existence of probability distributions of the Kolmogorov-type which was supposed by some authors is a mathematical…