Related papers: Deterministic Inequalities for Smooth M-estimators
Based on the idea of randomizing the traditional space theory of functional analysis, random functional analysis has been developed as functional analysis over random metric spaces, random normed modules and random locally convex modules.…
Heavy-tailed errors impair the accuracy of the least squares estimate, which can be spoiled by a single grossly outlying observation. As argued in the seminal work of Peter Huber in 1973 [{\it Ann. Statist.} {\bf 1} (1973) 799--821], robust…
We study maximum-likelihood-type estimation for diffusion processes when the coefficients are nonrandom and observation occurs in nonsynchronous manner. The problem of nonsynchronous observations is important when we consider the analysis…
In some estimation problems, especially in applications dealing with information theory, signal processing and biology, theory provides us with additional information allowing us to restrict the parameter space to a finite number of points.…
The maximum score method (Manski, 1975, 1985) is a powerful approach for binary choice models, yet it is known to face both practical and theoretical challenges. In particular, the estimator converges at a slower-than-root-$n$ rate to a…
Regression adjustment is broadly applied in randomized trials under the premise that it usually improves the precision of a treatment effect estimator. However, previous work has shown that this is not always true. To further understand…
We analyze a stochastic approximation algorithm for decision-dependent problems, wherein the data distribution used by the algorithm evolves along the iterate sequence. The primary examples of such problems appear in performative prediction…
For a broad class of nonlinear time series known as Bernoulli shifts, we establish the asymptotic normality of the smoothed periodogram estimator of the long-run variance. This estimator uses only a narrow band of Fourier frequencies around…
The maximum likelihood estimator (MLE) is pivotal in statistical inference, yet its application is often hindered by the absence of closed-form solutions for many models. This poses challenges in real-time computation scenarios,…
Let $\bx_j = \btheta +\bep_j, j=1,...,n$, be observations of an unknown parameter $\btheta$ in a Euclidean or separable Hilbert space $\scrH$, where $\bep_j$ are noises as random elements in $\scrH$ from a general distribution. We study the…
In this article we investigate consistency and asymptotic normality of the maximum likelihood and the posterior distribution of the parameters in the context of state space stochastic differential equations (SDEs). We then extend our…
Motivated by a wide variety of applications, ranging from stochastic optimization to dimension reduction through variable selection, the problem of estimating gradients accurately is of crucial importance in statistics and learning theory.…
We consider stochastic optimization problems with possibly nonsmooth integrands posed in Banach spaces and approximate these stochastic programs via a sample-based approaches. We establish the consistency of approximate Clarke stationary…
Existence and uniqueness as well as the iterative approximation of fixed points of enriched almost contractions in Banach spaces are studied. The obtained results are generalizations of the great majority of metric fixed point theorems, in…
A sum of observations derived by a simple random sampling design from a population of independent random variables is studied. A procedure finding a general term of Edgeworth asymptotic expansion is presented. The Lindeberg condition of…
In this paper, we analyze the finite sample complexity of stochastic system identification using modern tools from machine learning and statistics. An unknown discrete-time linear system evolves over time under Gaussian noise without…
We consider nonparametric estimation of a mixed discrete-continuous distribution under anisotropic smoothness conditions and possibly increasing number of support points for the discrete part of the distribution. For these settings, we…
This paper develops theory for feasible estimators of finite-dimensional parameters identified by general conditional quantile restrictions, under much weaker assumptions than previously seen in the literature. This includes instrumental…
Given a smooth function $f$, we develop a general approach to turn Monte Carlo samples with expectation $m$ into an unbiased estimate of $f(m)$. Specifically, we develop estimators that are based on randomly truncating the Taylor series…
In this paper, we present several new results on minimizing a nonsmooth and nonconvex function under a Lipschitz condition. Recent work shows that while the classical notion of Clarke stationarity is computationally intractable up to some…