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Functional data are smooth, often continuous, random curves, which can be seen as an extreme case of multivariate data with infinite dimensionality. Just as component-wise inference for multivariate data naturally performs feature selection, subset-wise inference for functional data performs domain selection. In this paper, we present a unified testing framework for domain selection on populations of functional data. In detail, p-values of hypothesis tests performed on point-wise evaluations of functional data are suitably adjusted for providing a control of the family-wise error rate (FWER) over a family of subsets of the domain. We show that several state-of-the-art domain selection methods fit within this framework and differ from each other by the choice of the family over which the control of the FWER is provided. In the existing literature, these families are always defined a priori. In this work, we also propose a novel approach, coined threshold-wise testing, in which the family of subsets is instead built in a data-driven fashion. The method seamlessly generalizes to multidimensional domains in contrast to methods based on a-priori defined families. We provide theoretical results with respect to consistency and control of the FWER for the methods within the unified framework. We illustrate the performance of the methods within the unified framework on simulated and real data examples, and compare their performance with other existing methods.

Nonparametric bagging clustering methods are studied and compared to identify latent structures from a sequence of dependent categorical data observed along a one-dimensional (discrete) time domain. The frequency of the observed categories is assumed to be generated by a (slowly varying) latent signal, according to latent state-specific probability distributions. The bagging clustering methods use random tessellations (partitions) of the time domain and clustering of the category frequencies of the observed data in the tessellation cells to recover the latent signal, within a bagging framework. New and existing ways of generating the tessellations and clustering are discussed and combined into different bagging clustering methods. Edge tessellations and adaptive tessellations are the new proposed ways of forming partitions. Composite methods are also introduced, that are using (automated) decision rules based on entropy measures to choose among the proposed bagging clustering methods. The performance of all the methods is compared in a simulation study. From the simulation study it can be concluded that local and global entropy measures are powerful tools in improving the recovery of the latent signal, both via the adaptive tessellation strategies (local entropy) and in designing composite methods (global entropy). The composite methods are robust and overall improve performance, in particular the composite method using adaptive (edge) tessellations.

The recent sports science literature conveys a growing interest in robust statistical methods to analyze smooth, regularly-sampled functional data. This paper focuses on the inferential problem of identifying the parts of a functional domain where two population means differ. We considered four approaches recently used in sports science: interval-wise testing (IWT), statistical parametric mapping (SPM), statistical nonparametric mapping (SnPM) and the Benjamini-Hochberg (BH) procedure for false discovery control. We applied these procedures to both six representative sports science datasets, and also to systematically varied simulated datasets which replicated ten signal- and/or noise-relevant parameters that were identified in the experimental datasets. We observed generally higher IWT and BH sensitivity for five of the six experimental datasets. BH was the most sensitive procedure in simulation, but also had relatively high false positive rates (generally > 0.1) which increased sharply (> 0.3) in certain extreme simulation scenarios including highly rough data. SPM and SnPM were more sensitive than IWT in simulation except for (1) high roughness, (2) high nonstationarity, and (3) highly nonuniform smoothness. These results suggest that the optimum procedure is both signal and noise-dependent. We conclude that: (1) BH is most sensitive but also susceptible to high false positive rates, (2) IWT, SPM and SnPM appear to have relatively inconsequential differences in terms of domain identification sensitivity, except in cases of extreme signal/noise characteristics, where IWT appears to be superior at identifying a greater portion of the true signal.

Here we present and compare functional and spatiotemporal (Sp.T.) kriging approaches to predict spatial functional random processes, which can also be viewed as Sp.T. random processes. Comparisons are focused on Sp.T. kriging versus ordinary kriging for functional data (OKFD), since more flexible functional kriging approaches like pointwise functional kriging and functional kriging total model coincide with OKFD in several situations. Prediction performance is evaluated via functional cross-validation on simulated data as well as on a Canadian weather data set. The two kriging approaches perform in many cases rather equal for stationary Sp.T. processes. For nonstationary Sp.T. processes, OKFD performs better than Sp.T. kriging. The computational time for OKFD is considerably lower compared to those for the Sp.T. kriging methods.

Fear of humans and its effect on animal behavior is increasingly being recognized as an important structuring force in ecological landscapes, with consequences for ecological interactions and communities. When aggressive, physically dominant species are displaced by anthropogenic disturbance, physically weaker species exploit competitor and predator downtimes to forage in previously risky places. Birds feeding at outdoor restaurants and cafés in association with humans are exposed to fluctuating levels of perceived danger caused by frequently changing densities of human diners. Consequently, birds must make decisions about which dining tables to visit based on trade-offs between foraging gain and perceived danger from avian competitors and humans. We tested the hypothesis that interspecific differences in response to perceived danger, combined with varying densities of human diners, dynamically alter which bird species predominates at dining tables. We found that house sparrows (Passer domesticus) tolerated higher human diner-densities than larger-sized, more physically dominant Eurasian jackdaws (Coloeus monedula). Sparrows were usually the first birds to visit diner-occupied tables and spent more time there than jackdaws. However, at diner-abandoned tables, this pattern changed: During low diner-densities at surrounding tables, jackdaws were usually the predominant species in first visits and minutes spent visiting, while at high diner-densities sparrows usually predominated. Moreover, along a gradient of increasing human diner-density, sparrows gradually replaced jackdaws as the predominant species in first visits and time at abandoned tables. However, at diner-occupied tables, once a sparrow chose which table to visit, factors other than diner-density influenced its choice of where to forage there (table-top or ground). To our knowledge, our research is the first scientific study of table-visiting behavior by birds at outdoor restaurants and cafés, and the first to reveal interspecific differences in table-visiting behavior by birds there.

One of the main concerns of silviculture and forest management focuses on finding fast, cost-efficient and non-destructive ways of measuring wood properties in standing trees. This paper presents an R package \verb+fiberLD+ that provides functions for estimating tree fiber length distributions in the standing tree based on increment core samples. The methods rely on increment core data measured by means of an optical fiber analyzer (OFA) or measured by microscopy. Increment core data analyzed by OFAs consist of the cell lengths of both cut and uncut fibers (tracheids) and fines (such as ray parenchyma cells) without being able to identify which cells are cut or if they are fines or fibers. The microscopy measured data consist of the observed lengths of the uncut fibers in the increment core. A censored version of a mixture of the fine and fiber length distributions is proposed to fit the OFA data, under distributional assumptions. Two choices for the assumptions of the underlying density functions of the true fiber (fine) lengths of those fibers (fines) that at least partially appear in the increment core are considered, such as the generalized gamma and the log normal densities. Maximum likelihood estimation is used for estimating the model parameters for both the OFA analyzed data and the microscopy measured data.