Related papers: Functional Analysis of Variance for Hilbert-Valued…

Classical finite mixture regression is useful for modeling the relationship between scalar predictors and scalar responses arising from subpopulations defined by the differing associations between those predictors and responses. Here we…

Reproducing kernel Hilbert spaces (RKHSs) are key spaces for machine learning that are becoming popular also for linear system identification. In particular, the so-called stable RKHSs can be used to model absolutely summable impulse…

This paper proposes a novel scheme for reduced-rank Gaussian process regression. The method is based on an approximate series expansion of the covariance function in terms of an eigenfunction expansion of the Laplace operator in a compact…

We formulate fractional difference equations of Riemann-Liouville and Caputo type in a functional analytical framework. Main results are existence of solutions on Hilbert space-valued weighted sequence spaces and a condition for stability…

The popular cubic smoothing spline estimate of a regression function arises as the minimizer of the penalized sum of squares $\sum_j(Y_j - {\mu}(t_j))^2 + {\lambda}\int_a^b [{\mu}"(t)]^2 dt$, where the data are $t_j,Y_j$, $j=1,..., n$. The…

In this article, we propose a penalized clustering method for large scale data with multiple covariates through a functional data approach. In the proposed method, responses and covariates are linked together through nonparametric…

Kernel mean embeddings, a widely used technique in machine learning, map probability distributions to elements of a reproducing kernel Hilbert space (RKHS). For supervised learning problems, where input-output pairs are observed, the…

With the widespread application of causal inference, it is increasingly important to have tools which can test for the presence of causal effects in a diverse array of circumstances. In this vein we focus on the problem of testing for…

We present an approach to defining Hilbert spaces of functions depending on infinitely many variables or parameters, with emphasis on a weighted tensor product construction based on stable space splittings, The construction has been used in…

The discussion focuses on metric covariance, a new association measure between paired random objects in a metric space, developed by Dubey and M\"uller, and on its relationship with other similar concepts which have previously appeared in…

Functional data that are nonnegative and have a constrained integral can be considered as samples of one-dimensional density functions. Such data are ubiquitous. Due to the inherent constraints, densities do not live in a vector space and,…

Motivated by recent work studying massive imaging data in the neuroimaging literature, we propose multivariate varying coefficient models (MVCM) for modeling the relation between multiple functional responses and a set of covariates. We…

Using the LRT statistic, a model R^2 is proposed for the generalized linear mixed model for assessing the association between the correlated outcomes and fixed effects. The R^2 compares the full model to a null model with all fixed effects…

In statistical learning, identifying underlying structures of true target functions based on observed data plays a crucial role to facilitate subsequent modeling and analysis. Unlike most of those existing methods that focus on some…

In this paper, we study an additive model where the response variable is Hilbert-space-valued and predictors are multivariate Euclidean, and both are possibly imperfectly observed. Considering Hilbert-space-valued responses allows to cover…

Classical regression analysis relates the expectation of a response variable to a linear combination of explanatory variables. In this article, we propose a covariance regression model that parameterizes the covariance matrix of a…

We consider an enlarged dimension reduction space in functional inverse regression. Our operator and functional analysis based approach facilitates a compact and rigorous formulation of the functional inverse regression problem. It also…

In this paper, we set up the theoretical foundations for a high-dimensional functional factor model approach in the analysis of large cross-sections (panels) of functional time series (FTS). We first establish a representation result…

A general formulation of the linear model with functional (random) explanatory variable $X = X(t), t \in T$ , and scalar response Y is proposed. It includes the standard functional linear model, based on the inner product in the space…

We propose a roughness regularization approach in making nonparametric inference for generalized functional linear models. In a reproducing kernel Hilbert space framework, we construct asymptotically valid confidence intervals for…