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Big data problems present great challenges to statisti-cal analyses, especially from the computational side. In this paper, we consider regression estimation of high-order mo-ments in big data problem...
In this paper we introduce a saddlepoint approximation method for higher-order moments like E(S − a) m+ ,a > 0, where the random variable S in these expectations could be a single random variabl...
An efficient estimator is constructed for the quadratic covariation or integrated covolatility matrix of a multivariate continuous martingale based on noisy and non-synchronous observations under high...
This article derives the first two moments of the two versions of the Riesz distribution in the terms of their characteristic functions.
We present formulas for the (raw and central) moments and absolute moments of the normal distribution. We note that these results are not new, yet many textbooks miss out on at least some of them. Hen...
Theorem 5.7 in [1] gives a formula for the variance of a minor (i.e., a sub-determinant) of a Wishart random matrix. The formula has to be corrected as follows.
A brief presentation of basics of the theory of Tchebycheff and Markov systems of functions and its applications to extremal problems for integrals of such functions is given.
We study the minimal sample size N=N(n) that suffices to estimate the covariance matrix of an n-dimensional distribution by the sample covariance matrix in the operator norm, and with an arbitrary fix...
Recently, Serfling and Xiao (2007) extended the L-moment theory (Hosking, 1990) to the multivariate setting.
Let X1,X2, . . . ,Xn be independent and identically distributed random variables. We present an analytic method for computing the moments of Sn = Pn i=1 Xi. The method is illustrated with a simple...
Using the classical estimation method of moments, we propose a new semiparametric estima- tion procedure for multi-parameter copula models. Consistency and asymptotic normality of the obtained estim...
We show how to compute lower bounds for the maximum possible Bayes error if the class-conditional distributions must satisfy moment constraints. Our approach makes use of Curto and Fialkow’s solution...
In the multiarmed bandit problem a gambler chooses an arm of a slot machine to pull considering a tradeoff between exploration and exploitation. We study the stochastic bandit problem where each arm...
This paper introduces a new parsimonious structure for mixture of autoregressive models. The weighting coefficients are determined through latent random variables, following a hidden Markov model. ...
Exact lower bounds on the exponential moments of min(y,X) and X I {X < y} are provided given the first two moments of a random variable X. These bounds are useful in work on large deviations probabi...

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