Related papers: On the uniform distribution modulo 1 of multidimen…
We establish the limiting spectral distribution of Kendall's correlation matrices in the moderate high-dimensional regime where the dimension grows slower than the sample size. Our framework allows observations to be independent but not…
This work concerns the nonlinear filtering problem of multiscale McKean-Vlasov stochastic systems where the whole systems depend on distributions of fast components. First of all, we prove that the slow component of the original system…
We propose a robust inferential procedure for assessing uncertainties of parameter estimation in high-dimensional linear models, where the dimension $p$ can grow exponentially fast with the sample size $n$. Our method combines the…
We prove the density hypothesis for congruence subgroups of an irreducible uniform lattice in $\mathrm{PSL}_2(\mathbb{R})^d$, extending previous results on the spherical density hypothesis to bound multiplicities of non-tempered…
We present the results of a realistic global fit of the Lagrangian parameters of the Minimal Supersymmetric Standard Model assuming universality for the first and second generation and real parameters. No assumptions on the SUSY breaking…
Datasets in high-dimension do not typically form clusters in their original space; the issue is worse when the number of points in the dataset is small. We propose a low-computation method to find statistically significant clustering…
In high-dimension, low-sample size (HDLSS) data, it is not always true that closeness of two objects reflects a hidden cluster structure. We point out the important fact that it is not the closeness, but the "values" of distance that…
A pressing problem for supersymmetry (SUSY) phenomenologists is how to incorporate Large Hadron Collider search results into parameter fits designed to measure or constrain the SUSY parameters. Owing to the computational expense of fully…
We introduce multilevel Picard (MLP) approximations for McKean--Vlasov stochastic differential equations (SDEs) with nonconstant diffusion coefficient. Under standard Lipschitz assumptions on the coefficients, we show that the MLP algorithm…
By facilitating the generation of samples from arbitrary probability distributions, Markov Chain Monte Carlo (MCMC) is, arguably, \emph{the} tool for the evaluation of Bayesian inference problems that yield non-standard posterior…
The statistical measure of spatial inhomogeneity for n points placed in chi cells each of size kxk is generalized to incorporate finite size objects like black pixels for binary patterns of size LxL. As a function of length scale k, the…
Given two distributions $\mathcal{P}$ and $\mathcal{Q}$ over a high-dimensional domain $\{0,1\}^n$, and a parameter $\varepsilon$, the goal of distance estimation is to determine the statistical distance between $\mathcal{P}$ and…
We are interested in strong approximations of one-dimensional SDEs which have non-Lipschitz coefficients and which take values in a domain. Under a set of general assumptions we derive an implicit scheme that preserves the domain of the…
In applications it is common that the exact form of a conditional expectation is unknown and having flexible functional forms can lead to improvements. Series method offers that by approximating the unknown function based on $k$ basis…
This paper constructs individual-specific density forecasts for a panel of firms or households using a dynamic linear model with common and heterogeneous coefficients as well as cross-sectional heteroskedasticity. The panel considered in…
Monte Carlo sampling has become a major vehicle for approximate inference in Bayesian networks. In this paper, we investigate a family of related simulation approaches, known collectively as quasi-Monte Carlo methods based on deterministic…
In this work, we extend results of Kakutani; Adler and Flatto; Smilansky; Pollicott and Sewell on the equidistribution of endpoints generated by interval-splitting procedures. We study a nonlinear version of the problem generated by a…
Here using some methods of combinatorial set theory, particularly the ones related to the construction of independent families of sets and some modified version of the notion of small sets originally introduced by Riecan, Riecan and…
Spatially coupled low-density parity-check codes show an outstanding performance under the low-complexity belief propagation (BP) decoding algorithm. They exhibit a peculiar convergence phenomenon above the BP threshold of the underlying…
We discuss the problem of defining an estimate for the error in quasi-Monte Carlo integration. The key issue is the definition of an ensemble of quasi-random point sets that, on the one hand, includes a sufficiency of equivalent point sets,…