Related papers: Statistical inferences for functional data
We present a functional data analysis approach for studying time-dependent, continuous glucose monitoring data with repeated measures for each individual in an experiment. After scaling the glucose concentration curves to the interval [0,…
We determine the expected error by smoothing the data locally. Then we optimize the shape of the kernel smoother to minimize the error. Because the optimal estimator depends on the unknown function, our scheme automatically adjusts to the…
We consider the problem of predicting a real random variable from a functional explanatory variable. The problem is attacked by mean of nonparametric kernel approach which has been recently adapted to this functional context. We derive…
We provide a theoretical foundation for non-parametric estimation of functions of random variables using kernel mean embeddings. We show that for any continuous function $f$, consistent estimators of the mean embedding of a random variable…
Classical multivariate principal component analysis has been extended to functional data and termed functional principal component analysis (FPCA). Most existing FPCA approaches do not accommodate covariate information, and it is the goal…
This paper discusses a general framework for smoothing parameter estimation for models with regular likelihoods constructed in terms of unknown smooth functions of covariates. Gaussian random effects and parametric terms may also be…
Functional data analysis has been extensively conducted. In this study, we consider a partially functional model, under which some covariates are scalars and have linear effects, while some other variables are functional and have…
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…
Recent technological developments have enabled us to collect complex and high-dimensional data in many scientific fields, such as population health, meteorology, econometrics, geology, and psychology. It is common to encounter such datasets…
Covariance estimation is ubiquitous in functional data analysis. Yet, the case of functional observations over multidimensional domains introduces computational and statistical challenges, rendering the standard methods effectively…
Longitudinal binary or count functional data are common in neuroscience, but are often too large to analyze with existing functional regression methods. We propose one-step penalized generalized estimating equations that supports…
We consider the problem of reconstructing missing data on a smooth manifold from incomplete and nonuniform samples. While classical methods for manifold approximation typically assume quasi-uniform data, their performance deteriorates…
New estimators for the mean and the covariance function for partially observed functional data are proposed using a detour via the fundamental theorem of calculus. The new estimators allow for a consistent estimation of the mean and…
Inference via simultaneous confidence band is studied for stationary covariance function of dense functional data. A two-stage estimation procedure is proposed based on spline approximation, the first stage involving estimation of all the…
We propose nonparametric methods for functional linear regression which are designed for sparse longitudinal data, where both the predictor and response are functions of a covariate such as time. Predictor and response processes have smooth…
We develop a group of robust, nonparametric hypothesis tests which detect differences between the covariance operators of several populations of functional data. These tests, called FKWC tests, are based on functional data depth ranks.…
This paper develops a framework for the estimation of the functional mean and the functional principal components when the functions form a random field. More specifically, the data we study consist of curves $X(\mathbf{s}_k;t),t\in[0,T]$,…
In this paper, we propose new semiparametric procedures for making inference on linear functionals and their functions of two semicontinuous populations. The distribution of each population is usually characterized by a mixture of a…
We propose a new framework for the simultaneous inference of monotone and smoothly time-varying functions under complex temporal dynamics. This will be done utilizing the monotone rearrangement and the nonparametric estimation. We…
We study the minimax estimation of covariance eigenfunctions and eigenvalues in functional principal component analysis when $n$ trajectories are observed at $p$ common grid points with additive noise. We consider covariance kernels with…