Functional data analysis (FDA), which is a branch of statistics on modeling infinite
dimensional random vectors resided in functional spaces, has become a major research …

The asymptotically correct confidence interval (CI) and simultaneous confidence band (SCB)
of any individual eigenvalue and eigenfunction are constructed under dense functional data …

We investigate statistical inference for functional time series by extending the classic
concept of an autocovariance function (ACF) to a functional ACF (FACF). We establish that …

Estimation and testing is studied for functional data with temporally dependent errors, an
interesting example of which is the event-related potential (ERP). B-spline estimators are …

We aim to develop simultaneous inference tools for the mean function of functional data from
sparse to dense. First, we derive a unified Gaussian approximation to construct …

The problem of constructing a simultaneous confidence band for the mean function of a
locally stationary functional time series $\{X_ {i, n}(t)\} _ {i= 1,\ldots, n} $ is challenging as …

Let f_1(t),\dots,f_n(t) be independent copies of some as continuous stochastic process f(t),
t∈0,1, which are observed with noise. We consider the problem of nonparametric estimation …

We propose a new bias-corrected spline-kernel estimator and a smooth simultaneous
confidence band (SCB) as a global inference tool for the conditional variance function in a …

A kernel distribution estimator (KDE) is proposed for the error distribution in the functional
data, which is computed from the residuals of the B-spline trajectories over all the …

A new two-step reconstruction-based moment estimator and an asymptotically correct
smooth simultaneous confidence band as a global inference tool are proposed for the …