Related papers: Variance inequalities for quadratic forms with app…
We prove large and moderate deviation principles for the distribution of an empirical mean conditioned by the value of the sum of discrete i.i.d. random variables. Some applications for combinatoric problems are discussed.
An algorithm is presented which generates pairs of oscillatory random time series which have identical periodograms but differ in the number of oscillations. This result indicate the intrinsic limitations of spectral methods when it comes…
We consider the problem of solving a large-scale Quadratically Constrained Quadratic Program. Such problems occur naturally in many scientific and web applications. Although there are efficient methods which tackle this problem, they are…
We provide non-asymptotic, relative deviation bounds for the eigenvalues of empirical covariance and Gram matrices in general settings. Unlike typical uniform bounds, which may fail to capture the behavior of smaller eigenvalues, our…
To estimate the conditional probability functions based on the direct problem setting, V-matrix based method was proposed. We construct V-matrix based constrained quadratic programming problems for which the inequality constraints are…
This work considers uncertainty relations on time frequency distributions from a signal processing viewpoint. An uncertainty relation on the marginalizable time frequency distributions is given. A result from quantum mechanics is used on…
In this paper, we study weakly nonlinear boundary value problems on infinite intervals. For such problems, we provide criteria for the existence of solutions as well as a qualitative description of the behavior of solutions depending on a…
We derive Cram\'{e}r type moderate deviations for stationary sequences of bounded random variables. Our results imply the moderate deviation principles and a Berry-Esseen bound. Applications to quantile coupling inequalities, functions of…
We consider the variance of a function of $n$ independent random variables and provide new inequalities which, in particular, extend previous results obtained for symmetric functions in the i.i.d.~setting. For instance, we obtain various…
We study the deviation inequality for the spectral norm of structured random matrices with non-gaussian entries. In particular, we establish an optimal bound for the $p$-th moment of the spectral norm by transfering the spectral norm into…
Random matrices have played an important role in many fields including machine learning, quantum information theory and optimization. One of the main research focuses is on the deviation inequalities for eigenvalues of random matrices.…
Random invariant manifolds are geometric objects useful for understanding complex dynamics under stochastic influences. Under a nonuniform hyperbolicity or a nonuniform exponential dichotomy condition, the existence of random pseudo-stable…
We consider a class of non-homogeneous Markov chains, that contains many natural examples. Next, using martingale methods, we establish some deviation and moment inequalities for separately Lipschitz functions of such a chain, under moment…
We explore the applications of our previously established likelihood-ratio method for deriving concentration inequalities for a wide variety of univariate and multivariate distributions. New concentration inequalities for various…
The aim of this paper is to provide conditions which ensure that the affinely transformed partial sums of a strictly stationary process converge in distribution to an infinite variance stable distribution. Conditions for this convergence to…
We introduce methods and theory for fractionally cointegrated curve time series. We develop a variance-ratio test to determine the dimensions associated with the nonstationary and stationary subspaces. For each subspace, we apply a local…
Statistical models that include random effects are commonly used to analyze longitudinal and correlated data, often with strong and parametric assumptions about the random effects distribution. There is marked disagreement in the literature…
We first prove some weighted inequalities for compositions of functions on time scales which are in turn applied to establish some new dynamic Opial-type inequalities in several variables. Some generalizations and applications to partial…
We study linear time fractional diffusion equations in divergence form of time order less than one. It is merely assumed that the coefficients are measurable and bounded, and that they satisfy a uniform parabolicity condition. As the main…
We survey some recent progress on rigorously establishing the universality of various spectral statistics of Wigner random matrix ensembles, focusing in particular on the Four Moment Theorem and its applications.