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Hypothesis testing is a key part of empirical science and multiple testing as well as the combination of evidence from several tests are continued areas of research. In this article we consider the problem of combining the results of multiple hypothesis tests to i) test global hypotheses and ii) make marginal inference while controlling the k-FWER. We propose a new family of combination tests for joint hypotheses, called the 'Too Many, Too Improbable' (TMTI) statistics, which we show through simulation to have higher power than other combination tests against many alternatives. Furthermore, we prove that a large family of combination tests -- which includes the one we propose but also other combination tests -- admits a quadratic shortcut when used in a Closed Testing Procedure, which controls the FWER strongly. We develop an algorithm that is linear in the number of hypotheses for obtaining confidence sets for the number of false hypotheses among a collection of hypotheses and an algorithm that is cubic in the number of hypotheses for controlling the k-FWER for any k greater than one.

Entomophthoralean fungi are insect pathogenic fungi and are characterized by their active discharge of infective conidia that infect insects. Our aim was to study the effects of temperature on the discharge and to characterize the variation in the associated temporal pattern of a newly discovered Pandora species with focus on peak location and shape of the discharge. Mycelia were incubated at various temperatures in darkness, and conidial discharge was measured over time. We used a novel modification of a statistical model (pavpop), that simultaneously estimates phase and amplitude effects, into a setting of generalized linear models. This model is used to test hypotheses of peak location and discharge of conidia. The statistical analysis showed that high temperature leads to an early and fast decreasing peak, whereas there were no significant differences in total number of discharged conidia. Using the proposed model we also quantified the biological variation in the timing of the peak location at a fixed temperature., Comment: 23 pages including supplementary material

We consider inference for misaligned multivariate functional data that represents the same underlying curve, but where the functional samples have systematic differences in shape. In this paper we introduce a new class of generally applicable models where warping effects are modeled through nonlinear transformation of latent Gaussian variables and systematic shape differences are modeled by Gaussian processes. To model cross-covariance between sample coordinates we introduce a class of low-dimensional cross-covariance structures suitable for modeling multivariate functional data. We present a method for doing maximum-likelihood estimation in the models and apply the method to three data sets. The first data set is from a motion tracking system where the spatial positions of a large number of body-markers are tracked in three-dimensions over time. The second data set consists of height and weight measurements for Danish boys. The third data set consists of three-dimensional spatial hand paths from a controlled obstacle-avoidance experiment. We use the developed method to estimate the cross-covariance structure, and use a classification setup to demonstrate that the method outperforms state-of-the-art methods for handling misaligned curve data., Comment: 44 pages in total including tables and figures. Additional 9 pages of supplementary material and references

A central task in the analysis of human movement behavior is to determine systematic patterns and differences across experimental conditions, participants and repetitions. This is possible because human movement is highly regular, being constrained by invariance principles. Movement timing and movement path, in particular, are linked through scaling laws. Separating variations of movement timing from the spatial variations of movements is a well-known challenge that is addressed in current approaches only through forms of preprocessing that bias analysis. Here we propose a novel nonlinear mixed-effects model for analyzing temporally continuous signals that contain systematic effects in both timing and path. Identifiability issues of path relative to timing are overcome by using maximum likelihood estimation in which the most likely separation of space and time is chosen given the variation found in data. The model is applied to analyze experimental data of human arm movements in which participants move a hand-held object to a target location while avoiding an obstacle. The model is used to classify movement data according to participant. Comparison to alternative approaches establishes nonlinear mixed-effects models as viable alternatives to conventional analysis frameworks. The model is then combined with a novel factor-analysis model that estimates the low-dimensional subspace within which movements vary when the task demands vary. Our framework enables us to visualize different dimensions of movement variation and to test hypotheses about the effect of obstacle placement and height on the movement path. We demonstrate that the approach can be used to uncover new properties of human movement., Comment: 30 pages, 21 figures and tables

Functional data analysis in a mixed-effects model framework is done using operator calculus. In this approach the functional parameters are treated as serially correlated effects giving an alternative to the penalized likelihood approach, where the functional parameters are treated as fixed effects. Operator approximations for the necessary matrix computations are proposed, and semi-explicit and numerically stable formulae of linear computational complexity are derived for likelihood analysis. The operator approach renders the usage of a functional basis unnecessary and clarifies the role of the boundary conditions., Comment: Published in at http://dx.doi.org/10.3150/11-BEJ389 the Bernoulli (http://isi.cbs.nl/bernoulli/) by the International Statistical Institute/Bernoulli Society (http://isi.cbs.nl/BS/bshome.htm)