Related papers: A Finite-Sample Deviation Bound for Stable Autoreg…
The purpose of this article is to develop a general parametric estimation theory that allows the derivation of the limit distribution of estimators in non-regular models where the true parameter value may lie on the boundary of the…
The objective of the present paper is to develop a minimax theory for the varying coefficient model in a non-asymptotic setting. We consider a high-dimensional sparse varying coefficient model where only few of the covariates are present…
We prove a limit theorem on the convergence of the distributions of the scaled last exit time over a slowly moving nonlinear boundary for a class of Gaussian stationary processes. The limit is a double exponential (Gumbel) distribution.
We establish maximal concentration bounds for the iterates generated by stochastic approximation algorithms with general step sizes, where the noise has a finite-state Markovian component plus a Martingale-difference component. When the…
The limiting behavior of Toeplitz type quadratic forms of stationary processes has received much attention through decades, particularly due to its importance in statistical estimation of the spectrum. In the present paper we study such…
We establish non-asymptotic bounds on the finite-sample behavior of generalized first-order iterative algorithms -- including gradient-based optimization methods and approximate message passing (AMP) -- with Gaussian data matrices and…
In this paper, an abstract framework for the error analysis of discontinuous finite element method is developed for the distributed and Neumann boundary control problems governed by the stationary Stokes equation with control constraints.…
Asymptotic expansions with explicit upper bounds for remainders are given for stationary distributions of nonlinearly perturbed semi-Markov processes with finite phase spaces. The corresponding algorithms are based on a special technique of…
We study rates of convergence in central limit theorems for the partial sum of squares of general Gaussian sequences, using tools from analysis on Wiener space. No assumption of stationarity, asymptotically or otherwise, is made. The main…
We analyze nonequilibrium fluctuations of the averaging process on $\mathbb T_\varepsilon^d$, a continuous degenerate Gibbs sampler running over the edges of the discrete $d$-dimensional torus. We show that, if we start from a smooth…
This note describes non-asymptotic variance and tail bounds for order statistics of samples of independent identically distributed random variables. Those bounds are checked to be asymptotically tight when the sampling distribution belongs…
We show bounds on tail probabilities for quadratic forms in sub-gaussian non-necessarily independent random variables. Our main tool will be estimates of the Luxemburg norms of such forms. This will allow us to formulate the above-mentioned…
The first purpose of this article is to obtain a.s. asymptotic properties of the maximum likelihood estimator in the autoregressive process driven by a stationary Gaussian noise. The second purpose is to show the local asymptotic normality…
A distributed average consensus algorithm in which every sensor transmits with bounded peak power is proposed. In the presence of communication noise, it is shown that the nodes reach consensus asymptotically to a finite random variable…
In a completely randomized experiment, the variances of treatment effect estimators in the finite population are usually not identifiable and hence not estimable. Although some estimable bounds of the variances have been established in the…
Maximizing the likelihood has been widely used for estimating the unknown covariance parameters of spatial Gaussian processes. However, evaluating and optimizing the likelihood function can be computationally intractable, particularly for…
We produce approximation bounds on a semidefinite programming relaxation for sparse principal component analysis. These bounds control approximation ratios for tractable statistics in hypothesis testing problems where data points are…
We develop and analyze stochastic inexact Gauss-Newton methods for nonlinear least-squares problems and for nonlinear systems ofequations. Random models are formed using suitable sampling strategies for the matrices involved in the…
We consider a simple mean reverting diffusion process, with piecewise constant drift and diffusion coefficients, discontinuous at a fixed threshold. We discuss estimation of drift and diffusion parameters from discrete observations of the…
We study time-uniform statistical inference for parameters in stochastic approximation (SA), which encompasses a bunch of applications in optimization and machine learning. To that end, we analyze the almost-sure convergence rates of the…