Related papers: A general asymptotic scheme for inference under or…
We consider kernel estimation of marginal densities and regression functions of stationary processes. It is shown that for a wide class of time series, with proper centering and scaling, the maximum deviations of kernel density and…
We obtain minimax-optimal convergence rates in the supremum norm, including information-theoretic lower bounds, for estimating the covariance kernel of a stochastic process which is repeatedly observed at discrete, synchronous design…
Regularly varying stochastic processes model extreme dependence between process values at different locations and/or time points. For such processes we propose a two-step parameter estimation of the extremogram, when some part of the domain…
Spaces of convex and concave functions appear naturally in theory and applications. For example, convex regression and log-concave density estimation are important topics in nonparametric statistics. In stochastic portfolio theory, concave…
Stochastic gradient descent is a classic algorithm that has gained great popularity especially in the last decades as the most common approach for training models in machine learning. While the algorithm has been well-studied when…
Sharp asymptotic lower bounds of the expected quadratic variation of discretization error in stochastic integration are given. The theory relies on inequalities for the kurtosis and skewness of a general random variable which are themselves…
Assume one observes independent categorical variables or, equivalently, one observes the corresponding multinomial variables. Estimating the distribution of the observed sequence amounts to estimating the expectation of the multinomial…
This study investigates the dynamics of alternating minimization applied to a bilinear regression task with normally distributed covariates, under the asymptotic system size limit where the number of parameters and observations diverge at…
We provide a means of computing and estimating the asymptotic distributions of statistics based on an outer minimization of an inner maximization. Such test statistics, which arise frequently in moment models, are of special interest in…
Distributed consensus optimization has received considerable attention in recent years; several distributed consensus-based algorithms have been proposed for (nonsmooth) convex and (smooth) nonconvex objective functions. However, the…
Consider a nonparametric regression model with one-sided errors and regression function in a general H\"older class. We estimate the regression function via minimization of the local integral of a polynomial approximation. We show uniform…
The change-plane Cox model is a popular tool for the subgroup analysis of survival data. Despite the rich literature on this model, there has been limited investigation into the asymptotic properties of the estimators of the…
We present a framework for the theoretical analysis of ensembles of low-complexity empirical risk minimisers trained on independent random compressions of high-dimensional data. First we introduce a general distribution-dependent…
We find the asymptotic distribution of the multi-dimensional multi-scale and kernel estimators for high-frequency financial data with microstructure. Sampling times are allowed to be asynchronous and endogenous. In the process, we show that…
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…
We consider distributed convex optimization problems originated from sample average approximation of stochastic optimization, or empirical risk minimization in machine learning. We assume that each machine in the distributed computing…
We consider the problem of adaptive inference on a regression function at a point under a multivariate nonparametric regression setting. The regression function belongs to a H\"older class and is assumed to be monotone with respect to some…
We study limit distributions of independent random matrices as well as limit joint distributions of their blocks under normalized partial traces composed with classical expectation. In particular, we are concerned with the ensemble of…
We study the central limit theorem in the non-normal domain of attraction to symmetric $\alpha$-stable laws for $0<\alpha\leq2$. We show that for i.i.d. random variables $X_i$, the convergence rate in $L^\infty$ of both the densities and…
In this paper, we propose a stochastic optimization method that adaptively controls the sample size used in the computation of gradient approximations. Unlike other variance reduction techniques that either require additional storage or the…