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In statistical physics and information theory, although the exponent of the partition function is often of our primary interest, there are cases where one needs more detailed information. In this paper, we present a general framework to…

This paper develops a new direct approach to approximating suprema of general empirical processes by a sequence of suprema of Gaussian processes, without taking the route of approximating whole empirical processes in the sup-norm. We prove…

The empirical copula process plays a central role in the asymptotic analysis of many statistical procedures which are based on copulas or ranks. Among other applications, results regarding its weak convergence can be used to develop…

Conformal prediction is a framework for predictive inference with a distribution-free, finite-sample guarantee. However, it tends to provide uninformative prediction sets when calibration data are scarce. This paper introduces…

We consider covariance parameter estimation for Gaussian processes with functional inputs. From an increasing-domain asymptotics perspective, we prove the asymptotic consistency and normality of the maximum likelihood estimator. We extend…

We introduce a new framework for constructing tests of general semiparametric hypotheses which have nontrivial power on the $n^{-1/2}$ scale in every direction, and can be tailored to put substantial power on alternatives of importance. The…

The paper discusses inference techniques for semiparametric models based on suitable versions of inference functions. The text contains two parts. In the first part, we review the optimality theory for non-parametric models based on the…

We present a numerically feasible semiclassical (SC) method to evaluate quantum fidelity decay (Loschmidt echo, FD) in a classically chaotic system. It was thought that such evaluation would be intractable, but instead we show that a…

We describe a simple method for making inference on a functional of a multivariate distribution. The method is based on a copula representation of the multivariate distribution and it is based on the properties of an Approximate Bayesian…

Testing for change points in sequences of covariance matrices is an important and equally challenging problem in statistical methodology with applications in various fields. Motivated by the observation that even in cases where the ratio…

The semiparametric factor model serves as a vital tool to describe the dependence patterns in the data. It recognizes that the common features observed in the data are actually explained by functions of specific exogenous variables.Unlike…

We study the large sample properties of sparse M-estimators in the presence of pseudo-observations. Our framework covers a broad class of semi-parametric copula models, for which the marginal distributions are unknown and replaced by their…

We consider the scenario where one observes an outcome variable and sets of features from multiple assays, all measured on the same set of samples. One approach that has been proposed for dealing with this type of data is ``sparse multiple…

We reconsider randomized algorithms for the low-rank approximation of symmetric positive semi-definite (SPSD) matrices such as Laplacian and kernel matrices that arise in data analysis and machine learning applications. Our main results…

Spatio-temporal covariances are important for describing the spatio-temporal variability of underlying random processes in geostatistical data. For second-order stationary processes, there exist subclasses of covariance functions that…

In this paper, we introduce Functional Generalized Canonical Correlation Analysis (FGCCA), a new framework for exploring associations between multiple random processes observed jointly. The framework is based on the multiblock Regularized…

In this paper, we study the estimation for a partial-linear single-index model. A two-stage estimation procedure is proposed to estimate the link function for the single index and the parameters in the single index, as well as the…

We consider subordinators $X_\alpha=(X_\alpha(t))_{t\ge 0}$ in the domain of attraction at 0 of a stable subordinator $(S_\alpha(t))_{t\ge 0}$ (where $\alpha\in(0,1)$); thus, with the property that $\overline{\Pi}_\alpha$, the tail function…

This article considers stochastic algorithms for efficiently solving a class of large scale non-linear least squares (NLS) problems which frequently arise in applications. We propose eight variants of a practical randomized algorithm where…

This paper provides convergence analysis for the approximation of a class of path-dependent functionals underlying a continuous stochastic process. In the first part, given a sequence of weak convergent processes, we provide a sufficient…