Variable selection in high-dimensional additive models based on norms of projections

We consider the problem of variable selection in high-dimensional sparse additive models. We focus on the case that the components belong to nonparametric classes of functions. The proposed method is motivated by geometric considerations in Hilbert spaces and consists of comparing the norms of the projections of the data onto various additive subspaces. Under minimal geometric assumptions, we prove concentration inequalities which lead to new conditions under which consistent variable selection is possible. As an application, we establish conditions under which a single component can be estimated with the rate of convergence corresponding to the situation in which the other components are known.Comment: 27 page

Lower bounds for invariant statistical models with applications to principal component analysis

This paper develops nonasymptotic information inequalities for the estimation of the eigenspaces of a covariance operator. These results generalize previous lower bounds for the spiked covariance model, and they show that recent upper bounds for models with decaying eigenvalues are sharp. The proof relies on lower bound techniques based on group invariance arguments which can also deal with a variety of other statistical models.Comment: 42 pages, to appear in Annales de l'Institut Henri Poincar\'e Probabilit\'es et Statistique

On the mod-Gaussian convergence of a sum over primes

We prove mod-Gaussian convergence for a Dirichlet polynomial which approximates $\operatorname{Im}\log\zeta(1/2+it)$. This Dirichlet polynomial is sufficiently long to deduce Selberg's central limit theorem with an explicit error term. Moreover, assuming the Riemann hypothesis, we apply the theory of the Riemann zeta-function to extend this mod-Gaussian convergence to the complex plane. From this we obtain that $\operatorname{Im}\log\zeta(1/2+it)$ satisfies a large deviation principle on the critical line. Results about the moments of the Riemann zeta-function follow.Comment: 22 pages, version accepted for publication in Math. Z., the final publication is available at link.springer.com/article/10.1007/s00209-013-1216-

Functional estimation and hypothesis testing in nonparametric boundary models

Consider a Poisson point process with unknown support boundary curve $g$, which forms a prototype of an irregular statistical model. We address the problem of estimating non-linear functionals of the form $\int \Phi(g(x))\,dx$. Following a nonparametric maximum-likelihood approach, we construct an estimator which is UMVU over H\"older balls and achieves the (local) minimax rate of convergence. These results hold under weak assumptions on $\Phi$ which are satisfied for $\Phi(u)=|u|^p$, $p\ge 1$. As an application, we consider the problem of estimating the $L^p$-norm and derive the minimax separation rates in the corresponding nonparametric hypothesis testing problem. Structural differences to results for regular nonparametric models are discussed.Comment: 21 pages, 1 figur

Relative perturbation bounds with applications to empirical covariance operators

The goal of this paper is to establish relative perturbation bounds, tailored for empirical covariance operators. Our main results are expansions for empirical eigenvalues and spectral projectors, leading to concentration inequalities and limit theorems. Our framework is very general, allowing for a huge variety of stationary, ergodic sequences, requiring only $p > 4$ moments. One of the key ingredients is a specific separation measure for population eigenvalues, which we call the relative rank. Developing a new algebraic approach for relative perturbations, we show that this relative rank gives rise to necessary and sufficient conditions for our concentration inequalities and limit theorems.Comment: 55 page

Fouled snails in flow:potential of epibionts on Littorina littorea to increase drag and reduce snail growth rates

Epibiosis is one of the closest interspecies associations. The presence of epibionts potentially causes a multitude of beneficial or detrimental effects for the basibiont. It has been shown previously that large epibionts may increase the risk of dislodgement of bivalves. In this study, sublethal effects of epibiont-induced drag increase are investigated. I assessed (1) the effects of common epibiont species (Balanus improvisus, Enteromorpha intestinalis, Ectocarpus sp.) on drag properties of the host (the periwinkle Littorina littorea), and (2) the long-term consequences of drag increase on growth rates of snails living in steady flow. All epibiont species increase drag on the host snail. They do so to unequal extents. This may be due to morphological and hydrodynamic differences among the epibionts. Thus, per unit volume of epibiont, the filamentous alga Ectocarpus sp, has a substantially stronger effect than the barnacles. Synergistic effects on drag increase can be observed in a mixed aufwuchs community. As compared to clean conspecifics, snails bearing artificial epibionts grow 35% more slowly when exposed to moderate, steady flow (8 cm s(-1)) for 5 mo. This difference in growth rates is enhanced when food is limited. I hypothesize that fouled snails coping with higher drag invest more energy into foot activities (muscles and mucus). As a consequence, when food is limited, growth rates decrease in fouled snails

Nachrichten von den Sternen im Meer

Woher kommen die Sterne im Meer, die man auch Seesterne nennt? Was können sie alles und warum sind ihre vielen Beine so wichtig, obwohl man sie fast nie laufen sieht? Wo ist eigentlich ihr Gehirn geblieben? - viele Fragen und ein paar Antworten zu schönen und wichtigen Meerestieren