Assessing extrema of empirical principal component functions

The difficulties of estimating and representing the distributions of functional data mean that principal component methods play a substantially greater role in functional data analysis than in more conventional finite-dimensional settings. Local maxima and minima in principal component functions are of direct importance; they indicate places in the domain of a random function where influence on the function value tends to be relatively strong but of opposite sign. We explore statistical properties of the relationship between extrema of empirical principal component functions, and their counterparts for the true principal component functions. It is shown that empirical principal component funcions have relatively little trouble capturing conventional extrema, but can experience difficulty distinguishing a ``shoulder'' in a curve from a small bump. For example, when the true principal component function has a shoulder, the probability that the empirical principal component function has instead a bump is approximately equal to 1/2. We suggest and describe the performance of bootstrap methods for assessing the strength of extrema. It is shown that the subsample bootstrap is more effective than the standard bootstrap in this regard. A ``bootstrap likelihood'' is proposed for measuring extremum strength. Exploratory numerical methods are suggested.Comment: Published at http://dx.doi.org/10.1214/009053606000000371 in the Annals of Statistics (http://www.imstat.org/aos/) by the Institute of Mathematical Statistics (http://www.imstat.org

Parameter tuning in pointwise adaptation using a propagation approach

This paper discusses the problem of adaptive estimation of a univariate object like the value of a regression function at a given point or a linear functional in a linear inverse problem. We consider an adaptive procedure originated from Lepski [Theory Probab. Appl. 35 (1990) 454--466.] that selects in a data-driven way one estimate out of a given class of estimates ordered by their variability. A serious problem with using this and similar procedures is the choice of some tuning parameters like thresholds. Numerical results show that the theoretically recommended proposals appear to be too conservative and lead to a strong oversmoothing effect. A careful choice of the parameters of the procedure is extremely important for getting the reasonable quality of estimation. The main contribution of this paper is the new approach for choosing the parameters of the procedure by providing the prescribed behavior of the resulting estimate in the simple parametric situation. We establish a non-asymptotical "oracle" bound, which shows that the estimation risk is, up to a logarithmic multiplier, equal to the risk of the "oracle" estimate that is optimally selected from the given family. A numerical study demonstrates a good performance of the resulting procedure in a number of simulated examples.Comment: Published in at http://dx.doi.org/10.1214/08-AOS607 the Annals of Statistics (http://www.imstat.org/aos/) by the Institute of Mathematical Statistics (http://www.imstat.org

Global smoothness estimation of a Gaussian process from regular sequence designs

We consider a real Gaussian process $X$ having a global unknown smoothness $(r_{\scriptscriptstyle 0},\beta_{\scriptscriptstyle 0})$, r_{\scriptscriptstyle 0}\in \mathds{N}_0 and $\beta_{\scriptscriptstyle 0} \in]0,1[$, with $X^{(r_{\scriptscriptstyle 0})}$ (the mean-square derivative of $X$ if $r_{\scriptscriptstyle 0}\ge 1$) supposed to be locally stationary with index $\beta_{\scriptscriptstyle 0}$. From the behavior of quadratic variations built on divided differences of $X$, we derive an estimator of $(r_{\scriptscriptstyle 0},\beta_{\scriptscriptstyle 0})$ based on - not necessarily equally spaced - observations of $X$. Various numerical studies of these estimators exhibit their properties for finite sample size and different types of processes, and are also completed by two examples of application to real data.Comment: 28 page

Assessing the number of mean-square derivatives of a Gaussian process

28 pagesInternational audienceWe consider a real Gaussian process $X$ with unknown smoothness \ro\in\n_{ßte 0} where the mean-square derivative X^{(\ro)} is supposed to be H\"{o}lder continuous in quadratic mean. First, from the discrete observations $X(t_1), \dotsc, X(t_n)$, we study reconstruction of $X(t)$, $t\in[0,1]$ with $\widetilde{X}_r(t)$, a piecewise polynomial interpolation of degree $r\ge 1$. We show that the mean-square error of interpolation is a decreasing function of $r$ but becomes stable as soon as r\ge \ro. Next, from an interpolation-based empirical criterion, we derive an estimator $\widehat{r}$ of \ro and prove its strong consistency by giving an exponential inequality for P(\widehat{r}\not=\ro). Finally, we prove the strong consistency of $\widetilde{X}_{\widehat{r}}(t)$ with an almost optimal rate

Flows at the Edge of an Active Region: Observation and Interpretation

Upflows observed at the edges of active regions have been proposed as the source of the slow solar wind. In the particular case of Active Region (AR) 10942, where such an upflow has been already observed, we want to evaluate the part of this upflow that actually remains confined in the magnetic loops that connect AR10942 to AR10943. Both active regions were visible simultaneously on the solar disk and were observed by STEREO/SECCHI EUVI. Using Hinode/EIS spectra, we determine the Doppler shifts and densities in AR10943 and AR10942, in order to evaluate the mass flows. We also perform magnetic field extrapolations to assess the connectivity between AR10942 and AR10943. AR10943 displays a persistent downflow in Fe XII. Magnetic extrapolations including both ARs show that this downflow can be connected to the upflow in AR10942. We estimate that the mass flow received by AR10943 areas connected to AR10942 represents about 18% of the mass flow from AR10942. We conclude that the upflows observed on the edge of active regions represent either large-scale loops with mass flowing along them (accounting for about one-fifth of the total mass flow in this example) or open magnetic field structures where the slow solar wind originates.Comment: 20 pages, 9 figures, accepted for publication in Astrophys.

Rapid and Efficient Methods to Isolate, Type Strains and Determine Species of Agrobacterium spp. in Pure Culture and Complex Environments

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Les choix organisationnels des propriétaires de chevaux de loisir dans les espaces ruraux

La possession d’équidés de loisir a récemment connu un essor important. Pour entretenir ces animaux, leurs propriétaires peuvent soit les prendre en charge eux-mêmes, soit faire appel à des prestataires de services marchands. Les assimilant à des producteurs de leur propre loisir, nous proposons d’étudier les déterminants de leur choix organisationnel grâce aux théories traitant habituellement des frontières de la firme. Les 251 enquêtes réalisées démontrent la pertinence de l’application de ces cadres d’analyse à la production domestique. Les propriétaires d’équidés poursuivent un objectif d’efficience. Ils cherchent à maximiser leur utilité, tout en minimisant leurs coûts de production et de transaction et en s’adaptant aux ressources auxquelles ils peuvent avoir accès.The number of recreational Equidae owners has recently increased sharply. These owners can choose between stabling and caring for their animals domestically, on their own property, or using professional service suppliers. By considering them as producers of their own leisure activity, we proposed to study the parameters involved in this choice using theories usually employed to analyze firm boundaries. Results from our 251 inquiries demonstrated the relevance of transposing these theoretical tools to domestic production. Equidae owners pursue an objective of efficiency. They aim at maximizing their utility while minimizing their production and transaction costs and adapting to resources they can access

Comparison of the cellular and biochemical properties of Plasmodium falciparum choline and ethanolamine kinases.

International audienceThe proliferation of the malaria-causing parasite Plasmodium falciparum within the erythrocyte is concomitant with massive phosphatidylcholine and phosphatidylethanolamine biosynthesis. Based on pharmacological and genetic data, de novo biosynthesis pathways of both phospholipids appear to be essential for parasite survival. The present study characterizes PfCK (P. falciparum choline kinase) and PfEK (P. falciparum ethanolamine kinase), which catalyse the first enzymatic steps of these essential metabolic pathways. Recombinant PfCK and PfEK were expressed as His6-tagged fusion proteins from overexpressing Escherichia coli strains, then purified to homogeneity and characterized. Using murine polyclonal antibodies against recombinant kinases, PfCK and PfEK were shown to be localized within the parasite cytoplasm. Protein expression levels increased during erythrocytic development. PfCK and PfEK appeared to be specific to their respective substrates and followed Michaelis-Menten kinetics. The Km value of PfCK for choline was 135.3+/-15.5 microM. PfCK was also able to phosphorylate ethanolamine with a very low affinity. PfEK was found to be an ethanolamine-specific kinase (Km=475.7+/-80.2 microM for ethanolamine). The quaternary ammonium compound hemicholinium-3 and an ethanolamine analogue, 2-amino-1-butanol, selectively inhibited PfCK or PfEK. In contrast, the bis-thiazolium compound T3, which was designed as a choline analogue and is currently in clinical trials for antimalarial treatment, affected PfCK and PfEK activities similarly. Inhibition exerted by T3 was competitive for both PfCK and PfEK and correlated with the impairment of cellular phosphatidylcholine biosynthesis. Comparative analyses of sequences and structures for both kinase types gave insights into their specific inhibition profiles and into the dual capacity of T3 to inhibit both PfCK and PfEK