Related papers: A maximal inequality for local empirical processes…

We study nonparametric distance-based (isotropic) local polynomial methods for estimating the boundary average treatment effect curve, a causal functional that captures treatment effect heterogeneity in boundary discontinuity designs. We…

We show that the cumulative distribution function corresponding to a kernel density estimator with optimal bandwidth lies outside any confidence interval, around the empirical distribution function, with probability tending to 1 as the…

We establish a functional limit law of the logarithm for the increments of the normed quantile process based upon a random sample of size $n\to\infty$. We extend a limit law obtained by Deheuvels and Mason (12), showing that their results…

Discovery problems often require deciding whether additional sampling is needed to detect all categories whose prevalence exceeds a prespecified threshold. We study this question under a Bernoulli product (incidence) model, where categories…

This study intends to introduce kernel mean embedding of probability measures over infinite-dimensional separable Hilbert spaces induced by functional response statistical models. The embedded function represents the concentration of…

Motivated by applications to the study of depth functions for tree-indexed random variables generated by point processes, we describe functional limit theorems for the intensity measure of point processes. Specifically, we establish uniform…

We establish a Harnack inequality for weak solutions of nonlocal equations in a disconnected region. The inequality compares the value of a solution on one connected component with its value on another, capturing a purely nonlocal…

We formulate a uniform tail bound for empirical processes indexed by a class of functions, in terms of the individual deviations of the functions rather than the worst-case deviation in the considered class. The tail bound is established by…

We obtain an almost sure bound for oscillation rates of empirical distribution functions for stationary causal processes. For short-range dependent processes, the oscillation rate is shown to be optimal in the sense that it is as sharp as…

The question of what can be computed, and how efficiently, are at the core of computer science. Not surprisingly, in distributed systems and networking research, an equally fundamental question is what can be computed in a…

Maximal inequalities refer to bounds on expected values of the supremum of averages of random variables over a collection. They play a crucial role in the study of non-parametric and high-dimensional estimators, and especially in the study…

This paper develops tests for inequality constraints of nonparametric regression functions. The test statistics involve a one-sided version of $L_p$-type functionals of kernel estimators $(1 \leq p < \infty)$. Drawing on the approach of…

This paper investigates robust versions of the general empirical risk minimization algorithm, one of the core techniques underlying modern statistical methods. Success of the empirical risk minimization is based on the fact that for a…

Let $(U_n(t))_{t\in\R^d}$ be the empirical process associated to an $\R^d$-valued stationary process $(X_i)_{i\ge 0}$. We give general conditions, which only involve processes $(f(X_i))_{i\ge 0}$ for a restricted class of functions $f$,…

Given a bounded class of functions G and independent random variables X1, . . . , Xn, we provide an upper bound for the expectation of the supremum of the empirical process over elements of G having a small variance. Our bound applies in…

We consider a time-varying first-order autoregressive model with irregular innovations, where we assume that the coefficient function is H\"{o}lder continuous. To estimate this function, we use a quasi-maximum likelihood based approach. A…

Given an observation of the uniform empirical process $\alp_n$, its functional increments $\alp_n(u+a_n\cdot)-\alp_n(u)$ can be viewed as a single random process, when $u$ is distributed under the Lebesgue measure. We investigate the almost…

We address the problem of learning an unknown smooth function and its derivatives from noisy pointwise evaluations under the supremum norm. While classical nonparametric regression provides a strong theoretical foundation, traditional…

We study the problem of empirical minimization for variance-type functionals over functional classes. Sharp non-asymptotic bounds for the excess variance are derived under mild conditions. In particular, it is shown that under some…

We present a systematic study on a class of nonlocal integral functionals for functions defined on a bounded domain and the naturally induced function spaces. The function spaces are equipped with a seminorm depending on finite differences…