Related papers: High-Order Statistical Functional Expansion and It…
Factor analysis for high-dimensional data is a canonical problem in statistics and has a wide range of applications. However, there is currently no factor model tailored to effectively analyze high-dimensional count responses with…
In a previous paper, dealing with "Applications in $\mathbb{R}^1$," the authors developed a new approach to the computation of the Hausdorff dimension of the invariant set of an iterated function system or IFS and studied some applications…
We present a numerical method for rigorous over-approximation of a reachable set of differential inclusions. The method gives high-order error bounds for single step approximations and a uniform bound on the error over the finite time…
We develop and implement a novel fast bootstrap for dependent data. Our scheme is based on the i.i.d. resampling of the smoothed moment indicators. We characterize the class of parametric and semi-parametric estimation problems for which…
We give analytic methods for nonparametric bias reduction that remove the need for computationally intensive methods like the bootstrap and the jackknife. We call an estimate {\it $p$th order} if its bias has magnitude $n_0^{-p}$ as $n_0…
While batching methods have been widely used in simulation and statistics, it is open regarding their higher-order coverage behaviors and whether one variant is better than the others in this regard. We develop techniques to obtain…
Tensor-valued data benefits greatly from dimension reduction as the reduction in size is exponential in the number of modes. To achieve maximal reduction without loss in information, our objective in this work is to give an automated…
Distributionally robust optimization (DRO) is a worst-case framework for stochastic optimization under uncertainty that has drawn fast-growing studies in recent years. When the underlying probability distribution is unknown and observed…
This paper studies the multi-task high-dimensional linear regression models where the noise among different tasks is correlated, in the moderately high dimensional regime where sample size $n$ and dimension $p$ are of the same order. Our…
For nearly a century and a half the Stokes phenomenon had been perceived as a discontinuous change in the asymptotic representation of a function. In 1989 Berry demonstrated how it is possible to smooth out this discontinuity in broad…
We review the Lyapunov functional method for linear ODEs and give an explicit construction of such functionals that yields sharp decay estimates, including an extension to defective ODE systems. As an application, we consider three…
We present a simple result that allows us to evaluate the asymptotic order of the remainder of a partial asymptotic expansion of the quantile function $h(u)$ as $u\to 0^+$ or $1^-$. This is focussed on important univariate distributions…
A higher-order numerical method is presented for scalar valued, coupled forward-backward stochastic differential equations. Unlike most classical references, the forward component is not only discretized by an Euler-Maruyama approximation…
We present a computationally efficient algorithm for stable numerical differentiation from noisy, uniformly-sampled data on a bounded interval. The method combines multi-interval Fourier extension approximations with an adaptive domain…
This paper focuses on the minimization of a sum of a twice continuously differentiable function $f$ and a nonsmooth convex function. An inexact regularized proximal Newton method is proposed by an approximation to the Hessian of $f$…
This paper presents a finite difference quasi-Newton method for the minimization of noisy functions. The method takes advantage of the scalability and power of BFGS updating, and employs an adaptive procedure for choosing the differencing…
We develop a uniform inference theory for high-dimensional slope parameters in threshold regression models, allowing for either cross-sectional or time series data. We first establish oracle inequalities for prediction errors, and L1…
In various statistical settings, the goal is to estimate a function which is restricted by the statistical model only through a conditional moment restriction. Prominent examples include the nonparametric instrumental variable framework for…
In this paper, we consider inference and uncertainty quantification for low Tucker rank tensors with additive noise in the high-dimensional regime. Focusing on the output of the higher-order orthogonal iteration (HOOI) algorithm, a commonly…
The article is devoted to the construction of explicit one-step numerical methods with the strong orders of convergence 2.0, 2,5, and 3.0 for Ito stochastic differential equations with multidimensional non-commutative noise. We consider the…