Related papers: Testing the Fractional Integration Parameter Revis…
Consider a big data multiple testing task, where, due to storage and computational bottlenecks, one is given a very large collection of p-values by splitting into manageable chunks and distributing over thousands of computer nodes. This…
In many experimental designs -- split-plots, blocked or nested layouts, fractional factorials, and studies with missing or unequal replication -- standard ANOVA procedures no longer tell us exactly how many independent pieces of information…
In the paper, we suggest three tests on the validity of a factor model which can be applied for both small dimensional and large dimensional data. Both the exact and asymptotic distributions of the resulting test statistics are derived…
We develop a unified approach for establishing rates of decay for the Fourier transform of a wide class of dynamically defined measures. Among the key features of the method is the systematic use of the $L^2$-flattening theorem obtained in…
In this article, we present a nonparametric method for the general two-sample problem involving functional random variables modelled as elements of a separable Hilbert space ${\cal H}$. First, we present a general recipe based on linear…
Thanks to its favorable properties, the multivariate normal distribution is still largely employed for modeling phenomena in various scientific fields. However, when the number of components $p$ is of the same asymptotic order as the sample…
Integrating evolutionary partial differential equations (PDEs) is an essential ingredient for studying the dynamics of the solutions. Indeed, simulations are at the core of scientific computing, but their mathematical reliability is often…
In many modern applications, a dependent functional response is observed for each subject over repeated time, leading to longitudinal functional data. In this paper, we propose a novel statistical procedure to test whether the mean function…
Testing independence is of significant interest in many important areas of large-scale inference. Using extreme-value form statistics to test against sparse alternatives and using quadratic form statistics to test against dense alternatives…
An important issue in functional time series analysis is whether an observed series comes from a purely random process. We extend the BDS test, a widely-used nonlinear independence test, to the functional time series. Like the BDS test in…
In this paper, we study two variations of the time discrete Taylor schemes for rough differential equations and for stochastic differential equations driven by fractional Brownian motions. One is the incomplete Taylor scheme which excludes…
We construct numerical integrators for Hamiltonian problems that may advantageously replace the standard Verlet time-stepper within Hybrid Monte Carlo and related simulations. Past attempts have often aimed at boosting the order of accuracy…
Partition of unity methods, such as the extended finite element method (XFEM) allow discontinuities to be simulated independently of the mesh [1]. This eliminates the need for the mesh to be aligned with the discontinuity or cumbersome…
In this note, we revisit the recent work of Diakonikolas, Gouleakis, Kane, Peebles, and Price (2021), and provide an alternative proof of their main result. Our argument does not rely on any specific property of Poisson random variables…
Citation numbers are extensively used for assessing the quality of scientific research. The use of raw citation counts is generally misleading, especially when applied to cross-disciplinary comparisons, since the average number of citations…
In this paper, we present a general framework for testing relevant hypotheses in functional time series. Our unified approach covers one-sample, two-sample, and change point problems under contaminated observations with arbitrary sampling…
Conditional independence (CI) is central to causal inference, feature selection, and graphical modeling, yet it is untestable in many settings without additional assumptions. Existing CI tests often rely on restrictive structural…
Replicability analysis aims to identify the findings that replicated across independent studies that examine the same features. We provide powerful novel replicability analysis procedures for two studies for FWER and for FDR control on the…
For spatially dependent functional data, a generalized Karhunen-Lo\`{e}ve expansion is commonly used to decompose data into an additive form of temporal components and spatially correlated coefficients. This structure provides a convenient…
Fractional derivatives can be used to model time delays in a diffusion process. When the order of the fractional derivative is distributed over the unit interval, it is useful for modeling a mixture of delay sources. In some special cases…