Related papers: Robust nonparametric hypothesis tests for differen…
In this paper, we consider the problem of estimating the eigenvalues and eigenfunctions of the covariance kernel (i.e., the functional principal components) from sparse and irregularly observed longitudinal data. We approach this problem…
Measurements of systems taken along a continuous functional dimension, such as time or space, are ubiquitous in many fields, from the physical and biological sciences to economics and engineering.Such measurements can be viewed as…
This study intends to introduce kernel mean embedding of probability measures over infinite-dimensional separable Hilbert spaces induced by functional response statistical models. The embedded function represents the concentration of…
We propose a novel kernel-based nonparametric two-sample test, employing the combined use of kernel mean and kernel covariance embedding. Our test builds on recent results showing how such combined embeddings map distinct probability…
We propose a novel test procedure for comparing mean functions across two groups within the reproducing kernel Hilbert space (RKHS) framework. Our proposed method is adept at handling sparsely and irregularly sampled functional data when…
This paper develops a framework for testing for associations in a possibly high-dimensional linear model where the number of features/variables may far exceed the number of observational units. In this framework, the observations are split…
Kernel methods, particularly kernel ridge regression (KRR), are time-proven, powerful nonparametric regression techniques known for their rich capacity, analytical simplicity, and computational tractability. The analysis of their predictive…
Kernel-based tests provide a simple yet effective framework that use the theory of reproducing kernel Hilbert spaces to design non-parametric testing procedures. In this paper we propose new theoretical tools that can be used to study the…
We consider functional linear regression models where functional outcomes are associated with scalar predictors by coefficient functions with shape constraints, such as monotonicity and convexity, that apply to sub-domains of interest. To…
We enlarge the number of available functional depths by introducing the kernelized functional spatial depth (KFSD). KFSD is a local-oriented and kernel-based version of the recently proposed functional spatial depth (FSD) that may be useful…
A vast amount of expert and domain knowledge is captured by causal structural priors, yet there has been little research on testing such priors for generalization and data synthesis purposes. We propose a novel model architecture, Causal…
Functional data analysis has attracted considerable interest and is facing new challenges, one of which is the increasingly available data in a streaming manner. In this article we develop an online nonparametric method to dynamically…
We define a numerical method that provides a non-parametric estimation of the kernel shape in symmetric multivariate Hawkes processes. This method relies on second order statistical properties of Hawkes processes that relate the covariance…
This paper examines the problem of nonparametric testing for the no-effect of a random covariate (or predictor) on a functional response. This means testing whether the conditional expectation of the response given the covariate is almost…
To the best of our knowledge, there are no general well-founded robust methods for statistical unsupervised learning. Most of the unsupervised methods explicitly or implicitly depend on the kernel covariance operator (kernel CO) or kernel…
We propose a class of kernel-based two-sample tests, which aim to determine whether two sets of samples are drawn from the same distribution. Our tests are constructed from kernels parameterized by deep neural nets, trained to maximize test…
Testing covariance structure is of importance in many areas of statistical analysis, such as microarray analysis and signal processing. Conventional tests for finite-dimensional covariance cannot be applied to high-dimensional data in…
The non-parametric estimation of covariance lies at the heart of functional data analysis, whether for curve or surface-valued data. The case of a two-dimensional domain poses both statistical and computational challenges, which are…
In this paper we review existing methods for robust functional principal component analysis (FPCA) and propose a new method for FPCA that can be applied to longitudinal data where only a few observations per trajectory are available. This…
Hypothesis testing for the slope function in functional linear regression is of both practical and theoretical interest. We develop a novel test for the nullity of the slope function, where testing the slope function is transformed into…