Related papers: Random Quadratic Forms with Dependence: Applicatio…
We present a sample- and time-efficient differentially private algorithm for ordinary least squares, with error that depends linearly on the dimension and is independent of the condition number of $X^\top X$, where $X$ is the design matrix.…
Binomial time series in which the logit of the probability of success is modelled as a linear function of observed regressors and a stationary latent Gaussian process are considered. Score tests are developed to first test for the existence…
Stochastic iterative methods are useful in a variety of large-scale numerical linear algebraic, machine learning, and statistical problems, in part due to their low-memory footprint. They are frequently used in a variety of applications,…
We study randomized variants of two classical algorithms: coordinate descent for systems of linear equations and iterated projections for systems of linear inequalities. Expanding on a recent randomized iterated projection algorithm of…
Patterned random matrices such as the reverse circulant, the symmetric circulant, the Toeplitz and the Hankel matrices and their almost sure limiting spectral distribution (LSD), have attracted much attention. Under the assumption that the…
Randomized algorithms, such as randomized sketching or stochastic optimization, are a promising approach to ease the computational burden in analyzing large datasets. However, randomized algorithms also produce non-deterministic outputs,…
We propose leave-out estimators of quadratic forms designed for the study of linear models with unrestricted heteroscedasticity. Applications include analysis of variance and tests of linear restrictions in models with many regressors. An…
The spatial linear mixed model (SLMM) consists of fixed and spatial random effects that may be linearly dependent. Partially motivated as a means to address potential issues with confounding, the Restricted spatial regression (RSR) model…
In compressed sensing, the "restricted isometry property" (RIP) is a sufficient condition for the efficient reconstruction of a nearly k-sparse vector x in C^d from m linear measurements Phi x. It is desirable for m to be small, and for Phi…
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…
Given a set of several inputs into a system (e.g., independent variables characterizing stimuli) and a set of several stochastically non-independent outputs (e.g., random variables describing different aspects of responses), how can one…
The exploration of associations between random objects with complex geometric structures has catalyzed the development of various novel statistical tests encompassing distance-based and kernel-based statistics. These methods have various…
Data-driven methods for modeling dynamic systems have received considerable attention as they provide a mechanism for control synthesis directly from the observed time-series data. In the absence of prior assumptions on how the time-series…
Regularly varying stochastic processes are able to model extremal dependence between process values at locations in random fields. We investigate the empirical extremogram as an estimator of dependence in the extremes. We provide conditions…
We study asymptotics of random shifted Young diagrams which correspond to a given sequence of reducible projective representations of the symmetric groups. We show limit results (Law of Large Numbers and Central Limit Theorem) for their…
Response-adaptive randomization has recently attracted a lot of attention in the literature. In this paper, we propose a new and simple family of response-adaptive randomization procedures that attain the Cramer--Rao lower bounds on the…
We consider the stochastic ranking process with space-time dependent jump rates for the particles. The process is a simplified model of the time evolution of the rankings such as sales ranks at online bookstores. We prove that the joint…
Quadratic variations of Gaussian processes play important role in both stochastic analysis and in applications such as estimation of model parameters, and for this reason the topic has been extensively studied in the literature. In this…
In this paper we present a series of results that permit to extend in a direct manner uniform deviation inequalities of the empirical process from the independent to the dependent case characterizing the additional error in terms of…
This paper presents new results allowing an unknown non-Gaussian positive matrix-valued random field to be identified through a stochastic elliptic boundary value problem, solving a statistical inverse problem. A new general class of…