Related papers: Methodology and Convergence Rates for Functional T…

We consider linear models with scalar responses and covariates from a separable Hilbert space. The aim is to detect change points in the error distribution, based on sequential residual empirical distribution functions. Expansions for those…

This paper studies the learning of linear operators between infinite-dimensional Hilbert spaces. The training data comprises pairs of random input vectors in a Hilbert space and their noisy images under an unknown self-adjoint linear…

We consider nonparametric functional regression when both predictors and responses are functions. More specifically, we let $(X_1,Y_1),...,(X_n,Y_n)$ be random elements in $\mathcal{F}\times\mathcal{H}$ where $\mathcal{F}$ is a semi-metric…

Hypothesis testing procedures are developed to assess linear operator constraints in function-on-scalar regression when incomplete functional responses are observed. The approach enables statistical inferences about the shape and other…

In data rich environments we may sometimes deal with time series that are probability density-function valued, such as observations of cross-sectional income distributions over time. To apply the methods of functional time series analysis…

We observe two sequences of curve which are connected via an integral operator. Our model includes linear models as well as autoregressive models in Hilbert spaces. We wish to test the null hypothesis that the operator did not change during…

The existing Fr\'echet regression is actually defined within a linear framework, since the weight function in the Fr\'echet objective function is linearly defined, and the resulting Fr\'echet regression function is identified to be a linear…

We consider regression models with parametric (linear or nonlinear) regression function and allow responses to be ``missing at random.'' We assume that the errors have mean zero and are independent of the covariates. In order to estimate…

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 consider a regression model that allows for time series covariates as well as heteroscedasticity with a regression function that is modelled nonparametrically. We assume that the regression function changes at some unknown…

In this paper, we propose a novel approach to fit a functional linear regression in which both the response and the predictor are functions of a common variable such as time. We consider the case that the response and the predictor…

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…

This paper addresses the problem of regression to reconstruct functions, which are observed with superimposed errors at random locations. We address the problem in reproducing kernel Hilbert spaces. It is demonstrated that the estimator,…

Linear autoregressive models serve as basic representations of discrete time stochastic processes. Different attempts have been made to provide non-linear versions of the basic autoregressive process, including different versions based on…

Robust estimation has played an important role in statistical and machine learning. However, its applications to functional linear regression are still under-developed. In this paper, we focus on Huber's loss with a diverging robustness…

Statistical analysis of high-dimensional functional times series arises in various applications. Under this scenario, in addition to the intrinsic infinite-dimensionality of functional data, the number of functional variables can grow with…

We consider nonparametric estimation of the mean and covariance functions for functional/longitudinal data. Strong uniform convergence rates are developed for estimators that are local-linear smoothers. Our results are obtained in a unified…

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…

In this paper, we study nonparametric models allowing for locally stationary regressors and a regression function that changes smoothly over time. These models are a natural extension of time series models with time-varying coefficients. We…

Regression models with a response variable taking values in a Hilbert space and hybrid covariates are considered. This means two sets of regressors are allowed, one of finite dimension and a second one functional with values in a Hilbert…