This paper is devoted to nonparametric analysis of functional data. We give asymptotic results for a kNN generalized regression estimator when the observed variables take values in any abstract space. The main novelty is our uniform consistency result (with rates).

Constructing generative models for functional observations is an important task in statistical functional analysis. In general, functional data contains both phase (or x or horizontal) and amplitude (or y or vertical) variability. Traditional methods often ignore the phase variability and focus...

We develop a doubly spectral representation of a stationary functional time series, and study the properties of its empirical version. The representation decomposes the time series into an integral of uncorrelated frequency components (Cramér representation), each of which is in turn expanded...

The past few years have highlighted the need to protect diversity in its broader concept and, in particular, with reference to the ecological context for environmental protection. In this context, the problem of the definition and the measurement of diversity becomes fundamental. This paper...

Suppose we observe a Markov chain taking values in a functional space. We are interested in exploiting the time series dependence in these infinite dimensional data in order to make non-trivial predictions about the future. Making use of the Karhunen–Loève (KL) representation of functional...

Functional analysis of variance involves testing for differences in functional means across k groups in n functional responses. If a significant overall difference in the mean curves is detected, one may want to identify the location of these differences. Cox and Lee (2008) proposed performing a...