Related papers: Functional Linear Regression: Dependence and Error…
Tests for structural breaks in time series should ideally be sensitive to breaks in the parameter of interest, while being robust to nuisance changes. Statistical analysis thus needs to allow for some form of nonstationarity under the null…
We consider nonparametric regression with functional covariates, that is, they are elements of an infinite-dimensional Hilbert space. A locally polynomial estimator is constructed, where an orthonormal basis and various tuning parameters…
In the last few decades, building regression models for non-scalar variables, including time series, text, image, and video, has attracted increasing interests of researchers from the data analytic community. In this paper, we focus on a…
Many fMRI analyses examine functional connectivity, or statistical dependencies among remote brain regions. Yet popular methods for studying whole-brain functional connectivity often yield results that are difficult to interpret. Factor…
Functional linear regression is one of the fundamental and well-studied methods in functional data analysis. In this work, we investigate the functional linear regression model within the context of reproducing kernel Hilbert space by…
We consider estimation of mean and covariance functions of functional snippets, which are short segments of functions possibly observed irregularly on an individual specific subinterval that is much shorter than the entire study interval.…
As medical devices become more complex, they routinely collect extensive and complicated data. While classical regressions typically examine the relationship between an outcome and a vector of predictors, it becomes imperative to identify…
In this paper, we propose a covariate-adjusted nonlinear regression model. In this model, both the response and predictors can only be observed after being distorted by some multiplicative factors. Because of nonlinearity, existing methods…
Gaussian processes that can be decomposed into a smooth mean function and a stationary autocorrelated noise process are considered and a fully automatic nonparametric method to simultaneous estimation of mean and auto-covariance functions…
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 many longitudinal settings, time-varying covariates may not be measured at the same time as responses and are often prone to measurement error. Naive last-observation-carried-forward methods incur estimation biases, and existing…
We consider the estimation of the value of a linear functional of the slope parameter in functional linear regression, where scalar responses are modeled in dependence of random functions. In Johannes and Schenk [2010] it has been shown…
A characteristic feature of functional data is the presence of phase variability in addition to amplitude variability. Existing functional regression methods do not handle time variability in an explicit and efficient way. In this paper we…
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…
Traditional functional linear regression usually takes a one-dimensional functional predictor as input and estimates the continuous coefficient function. Modern applications often generate two-dimensional covariates, which become matrices…
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…
We develop methodology to detect structural breaks in the slope function of a concurrent functional linear regression model for functional time series in $C[0,1]$. Our test is based on a CUSUM process of regressor-weighted OLS residual…
Additive models play an essential role in studying non-linear relationships. Despite many recent advances in estimation, there is a lack of methods and theories for inference in high-dimensional additive models, including confidence…
Functional data analysis is a fast evolving branch of statistics. Estimation procedures for the popular functional linear model either suffer from lack of robustness or are computationally burdensome. To address these shortcomings, a…
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…