Related papers: High Dimensional Bootstrap and Asymptotic Expansio…
We consider second order explicit and implicit two-step time-discrete schemes for wave-type equations. We derive optimal order aposteriori estimates controlling the time discretization error. Our analysis, has been motivated by the need to…
Let ${X}_{k}=(x_{k1}, \cdots, x_{kp})', k=1,\cdots,n$, be a random sample of size $n$ coming from a $p$-dimensional population. For a fixed integer $m\geq 2$, consider a hypercubic random tensor $\mathbf{{T}}$ of $m$-th order and rank $n$…
The bootstrap variance estimate is widely used in semiparametric inferences. However, its theoretical validity is a well known open problem. In this paper, we provide a {\em first} theoretical study on the bootstrap moment estimates in…
In this paper we investigate how the bootstrap can be applied to time series regressions when the volatility of the innovations is random and non-stationary. The volatility of many economic and financial time series displays persistent…
This paper develops bootstrap procedures for inference in linear regression models with two-way clustered data. We characterize the estimator's asymptotic behavior in five mutually exclusive and exhaustive regimes: three Gaussian and two…
In this paper, we present approximation algorithms for combinatorial optimization problems under probabilistic constraints. Specifically, we focus on stochastic variants of two important combinatorial optimization problems: the k-center…
This paper considers inference for conditional moment inequality models using a multiscale statistic. We derive the asymptotic distribution of this test statistic and use the result to propose feasible critical values that have a simple…
The class of complex random vectors whose covariance matrix is linearly parameterized by a basis of Hermitian Toeplitz (HT) matrices is considered, and the maximum compression ratios that preserve all second-order information are derived…
A variational method is discussed, extending the Gaussian effective potential to higher orders. The single variational parameter is replaced by trial unknown two-point functions, with infinite variational parameters to be optimized by the…
In this paper, we study stochastic non-convex optimization with non-convex random functions. Recent studies on non-convex optimization revolve around establishing second-order convergence, i.e., converging to a nearly second-order optimal…
We give an order-explicit large deviation bound for the difference between a high-dimensional $U$-statistic and its H\'{a}jek projection. In particular, we show that any $U$-statistic of order $b$ on $n$ observations, with a $d$-dimensional…
Student's $t$ statistic is finding applications today that were never envisaged when it was introduced more than a century ago. Many of these applications rely on properties, for example robustness against heavy tailed sampling…
We consider chance-constrained binary knapsack problems, where the weights of items are independent random variables with the means and standard deviations known. The chance constraint can be reformulated as a second-order cone constraint…
The maximum-likelihood estimator of nonlinear panel data models with fixed effects is consistent but asymptotically-biased under rectangular-array asymptotics. The literature has thus far concentrated its effort on devising methods to…
This article establishes novel strong uniform laws of large numbers for randomly weighted sums such as bootstrap means. By leveraging recent advances, these results extend previous work in their general applicability to a wide range of…
We study generalized bootstrap confidence regions for the mean of a random vector whose coordinates have an unknown dependency structure. The random vector is supposed to be either Gaussian or to have a symmetric and bounded distribution.…
Although the operator (spectral) norm is one of the most widely used metrics for covariance estimation, comparatively little is known about the fluctuations of error in this norm. To be specific, let $\hat\Sigma$ denote the sample…
The block bootstrap approximates sampling distributions from dependent data by resampling data blocks. A fundamental problem is establishing its consistency for the distribution of a sample mean, as a prototypical statistic. We use a…
We study the maximum $k$-set coverage problem in the following distributed setting. A collection of sets $S_1,\ldots,S_m$ over a universe $[n]$ is partitioned across $p$ machines and the goal is to find $k$ sets whose union covers the most…
Bootstrap percolation on a graph is a deterministic process that iteratively enlarges a set of occupied sites by adjoining points with at least $\theta$ occupied neighbors. The initially occupied set is random, given by a uniform product…