Related papers: Limit theorems for filtered long-range dependent r…
In this paper, we focus on studying central limit theorems for functionals of some specific stationary random processes. In classical probability theory, it is well-known that for non-linear functionals of stationary Gaussian sequences, we…
We develop technique concerning statistical analyses of the large-scale structure of the universe in the presence of biasing in the structure formation. We formulate the diagrammatic method to calculate the correlation functions of the…
We consider the problem of bounding large deviations for non-i.i.d. random variables that are allowed to have arbitrary dependencies. Previous works typically assumed a specific dependence structure, namely the existence of independent…
We consider the Bayesian analysis of models in which the unknown distribution of the outcomes is specified up to a set of conditional moment restrictions. The nonparametric exponentially tilted empirical likelihood function is constructed…
We prove empirical central limit theorems for the distribution of levels of various random fields defined on high-dimensional discrete structures as the dimension of the structure goes to $\infty$. The random fields considered include costs…
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…
Boundedness properties of operators associated with non-degenerate symmetric $\alpha$-stable, $\alpha \in (1,2)$, probability measures on $\mathbb{R}^d$ are investigated on appropriate, Euclidean or otherwise, $L^p$-spaces, $p \in…
This paper provides a unified framework for analyzing tensor estimation problems that allow for nonlinear observations, heteroskedastic noise, and covariate information. We study a general class of high-dimensional models where each…
This paper establishes a central limit theorem and an invariance principle for a wide class of stationary random fields under natural and easily verifiable conditions. More precisely, we deal with random fields of the form $X_k =…
The filtering distribution is a time-evolving probability distribution on the state of a dynamical system, given noisy observations. We study the large-time asymptotics of this probability distribution for discrete-time, randomly…
We analyze the macroscopic behavior of multi-populations randomly connected neural networks with interaction delays. Similar to cases occurring in spin glasses, we show that the sequences of empirical measures satisfy a large deviation…
I study partial identification of distributional parameters in triangular systems. This model consists of a nonparametric outcome equation and a selection equation. This allows for general unobserved heterogeneity and selection on…
We consider whether the non-Gaussian scale-dependent halo bias can be used not only to constrain the local form of non-Gaussianity but also to distinguish among different shapes. In particular, we ask whether it can constrain the behavior…
We revisit the problem of estimating the parameters of a partially observed diffusion process, consisting of a hidden state process and an observed process, with a continuous time parameter. The estimation is to be done online, i.e. the…
The super-parametric density estimators and its related algorism were suggested by Y. -S. Tsai et al [7]. The number of parameters is unlimited in the super- parametric estimators and it is a general theory in sense of unifying or…
We generalize a recent model-independent form factor parameterization derived from rigorous dispersion relations to include constraints from data in the timelike region. These constraints dictate the convergence properties of the…
Fractal behavior and long-range dependence have been observed in an astonishing number of physical systems. Either phenomenon has been modeled by self-similar random functions, thereby implying a linear relationship between fractal…
Concentration inequalities are widely used for analyzing machine learning algorithms. However, current concentration inequalities cannot be applied to some of the most popular deep neural networks, notably in natural language processing.…
We analyze the posterior contraction rates of parameters in Bayesian models via the Langevin diffusion process, in particular by controlling moments of the stochastic process and taking limits. Analogous to the non-asymptotic analysis of…
We study diffusion of particles in large-scale simulations of one-dimensional stochastic sandpiles, in both the restricted and unrestricted versions. The results indicate that the diffusion constant scales in the same manner as the activity…