Related papers: Estimating non-linear functionals of trawl process…

In this paper, we develop a new and effective approach to nonparametric quantile regression that accommodates ultrahigh-dimensional data arising from spatio-temporal processes. This approach proves advantageous in staving off computational…

The asymptotic analysis of covariance parameter estimation of Gaussian processes has been subject to intensive investigation. However, this asymptotic analysis is very scarce for non-Gaussian processes. In this paper, we study a class of…

We prove a sequence of limiting results about weakly dependent stationary and regularly varying stochastic processes in discrete time. After deducing the limiting distribution for individual clusters of extremes, we present a new type of…

We address the problem of continual learning in multi-task Gaussian process (GP) models for handling sequential input-output observations. Our approach extends the existing prior-posterior recursion of online Bayesian inference, i.e.\ past…

We consider the problem of constructing confidence intervals for nonparametric functional data analysis using empirical likelihood. In this doubly infinite-dimensional context, we demonstrate the Wilks's phenomenon and propose a…

This paper presents a Gaussian process (GP) model for estimating piecewise continuous regression functions. In scientific and engineering applications of regression analysis, the underlying regression functions are piecewise continuous in…

Computing accurate estimates of the Fourier transform of analog signals from discrete data points is important in many fields of science and engineering. The conventional approach of performing the discrete Fourier transform of the data…

Currently, the high-precision estimation of nonlinear parameters such as Gini indices, low-income proportions or other measures of inequality is particularly crucial. In the present paper, we propose a general class of estimators for such…

We construct flexible likelihoods for multi-output Gaussian process models that leverage neural networks as components. We make use of sparse variational inference methods to enable scalable approximate inference for the resulting class of…

In nonlinear latent variable models or dynamic models, if we consider the latent variables as confounders (common causes), the noise dependencies imply further relations between the observed variables. Such models are then closely related…

In functional data analysis (FDA), covariance function is fundamental not only as a critical quantity for understanding elementary aspects of functional data but also as an indispensable ingredient for many advanced FDA methods. This paper…

Bagging is a useful method for large-scale statistical analysis, especially when the computing resources are very limited. We study here the asymptotic properties of bagging estimators for $M$-estimation problems but with massive datasets.…

We look into the nonparametric regression estimation with additive and multiplicative noise and construct adaptive thresholding estimators based on Laguerre series. The proposed approach achieves asymptotically near-optimal convergence…

Many biological characteristics of evolutionary interest are not scalar variables but continuous functions. Given a dataset of function-valued traits generated by evolution, we develop a practical statistical approach to infer ancestral…

We develop nonlinear renewal theorems for a perturbed random walk without assuming stochastic boundedness of centered perturbation terms. A second order expansion of the expected stopping time is obtained via the uniform integrability of…

We address the challenge of estimation in the context of constant linear effect models with dense functional responses. In this framework, the conditional expectation of the response curve is represented by a linear combination of…

Distinguishing active from passive dynamics is a fundamental challenge in understanding the motion of living cells and other active matter systems. Here, we introduce a framework that combines physical modeling, analytical theory, and…

When a probe particle immersed in a fluid with nonlinear interactions is subject to strong driving, the cumulants of the stochastic force acting on the probe are nonlinear functionals of the driving protocol. We present a Volterra series…

The paper studies the asymptotic behaviour of weighted functionals of long-range dependent data over increasing observation windows. Various important statistics, including sample means, high order moments, occupation measures can be given…

The problem of estimating a linear functional based on observational data is canonical in both the causal inference and bandit literatures. We analyze a broad class of two-stage procedures that first estimate the treatment effect function,…