相关论文: Minimax estimation of Functional Principal Compone…
Regularity estimates for an integral operator with a symmetric continuous kernel on a convex bounded domain are derived. The covariance of a mean-square continuous random field on the domain is an example of such an operator. The estimates…
This work aims at performing Functional Principal Components Analysis (FPCA) with Horvitz-Thompson estimators when the observations are curves collected with survey sampling techniques. One important motivation for this study is that FPCA…
Non-parametric inference for functional data over two-dimensional domains entails additional computational and statistical challenges, compared to the one-dimensional case. Separability of the covariance is commonly assumed to address these…
In many areas of science one aims to estimate latent sub-population mean curves based only on observations of aggregated population curves. By aggregated curves we mean linear combination of functional data that cannot be observed…
Contamination of covariates by measurement error is a classical problem in multivariate regression, where it is well known that failing to account for this contamination can result in substantial bias in the parameter estimators. The nature…
High-dimensional statistical tests often ignore correlations to gain simplicity and stability leading to null distributions that depend on functionals of correlation matrices such as their Frobenius norm and other $\ell_r$ norms. Motivated…
We study a problem of estimation of smooth functionals of parameter $\theta $ of Gaussian shift model $$ X=\theta +\xi,\ \theta \in E, $$ where $E$ is a separable Banach space and $X$ is an observation of unknown vector $\theta$ in Gaussian…
We consider the prediction problem of a continuous-time stochastic process on an entire time-interval in terms of its recent past. The approach we adopt is based on functional kernel nonparametric regression estimation techniques where…
We study the optimal estimation of probability matrices of random graph models generated from graphons. This problem has been extensively studied in the case of step-graphons and H\"older smooth graphons. In this work, we characterize the…
In supervised learning, the output variable to be predicted is often represented as a function, such as a spectrum or probability distribution. Despite its importance, functional output regression remains relatively unexplored. In this…
In practice, observations are often contaminated by noise, making the resulting sample covariance matrix to be an information-plus-noise-type covariance matrix. Aiming to make inferences about the spectra of the underlying true covariance…
Estimation of the covariance structure of spatial processes is of fundamental importance in spatial statistics. In the literature, several non-parametric and semi-parametric methods have been developed to estimate the covariance structure…
Multi-dimensional Hawkes process (MHP) is a class of self and mutually exciting point processes that find wide range of applications -- from prediction of earthquakes to modelling of order books in high frequency trading. This paper makes…
In this work we study the self-integral of a function-measure kernel and its importance on stochastic integration. A continuous-function measure kernel $K$ over $D \subset \mathbb{R}^{d}$ is a function of two variables which acts as a…
In nonparametric regression analysis, errors are possibly correlated in practice, and neglecting error correlation can undermine most bandwidth selection methods. When no prior knowledge or parametric form of the correlation structure is…
We consider nonparametric estimation of a covariance function on the unit square, given a sample of discretely observed fragments of functional data. When each sample path is only observed on a subinterval of length $\delta<1$, one has no…
We derive an estimator of the spectral density of a functional time series that is the output of a multilayer perceptron neural network. The estimator is motivated by difficulties with the computation of existing spectral density estimators…
Second-order characteristics including covariance and spectral density functions are fundamentally important for both statistical applications and theoretical analysis in functional time series. In the high-dimensional setting where the…
Many economic parameters are identified by ``thin sets'' (submanifolds with Lebesgue measure zero) and hence difficult to recover from data in an ambient space. This paper provides a unified theory for estimation and inference of such…
In this paper we focus on the linear functionals defining an approximate version of the gradient of a function. These functionals are often used when dealing with optimization problems where the computation of the gradient of the objective…