Marek Omelka

Improved kernel estimation of copulas: Weak convergence and goodness-of-fit testing

We reconsider the existing kernel estimators for a copula function, as proposed in Gijbels and Mielniczuk [Comm. Statist. Theory Methods 19 (1990) 445-464], Fermanian, Radulovic and Wegkamp [Bernoulli 10 (2004) 847-860] and Chen and Huang [Canad. J. Statist. 35 (2007) 265-282]. All of these estimators have as a drawback that they can suffer from a comer bias problem. A way to deal with this is to impose rather stringent conditions on the copula, outruling as such many classical families of copulas. In this paper, we propose improved estimators that take care of the typical corner bias problem. For Gijbels and Mielniczuk [Comm. Statist. Theory Methods 19 (1990) 445-464] and Chen and Huang [Canad. J. Statist. 35 (2007) 265-282], the improvement involves shrinking the bandwidth with an appropriate functional factor; for Fermanian, Radulovic and Wegkamp [Bernoulli 10 (2004) 847-860], this is done by using a transformation. The theoretical contribution of the paper is a weak convergence result for the three improved estimators under conditions that are met for most copula families. We also discuss the choice of bandwidth parameters, theoretically and practically, and illustrate the finite-sample behaviour of the estimators in a simulation study. The improved estimators are applied to goodness-of-fit testing for copulas.

Detection of residual B precursor lymphoblastic leukemia by uniform gating flow cytometry

Residual disease (RD) is an important prognostic factor in acute lymphoblastic leukemia (ALL). Flow cytometry (FC)‐based RD detection is easy to perform, but interpretation requires expert analysis due to individual differences among patients.

Development of Methods for Cross-Sectional HIV Incidence Estimation in a Large, Community Randomized Trial

Background Accurate methods of HIV incidence determination are critically needed to monitor the epidemic and determine the population level impact of prevention trials. One such trial, Project Accept, a Phase III, community-randomized trial, evaluated the impact of enhanced, community-based voluntary counseling and testing on population-level HIV incidence. The primary endpoint of the trial was based on a single, cross-sectional, post-intervention HIV incidence assessment. Methods and Findings Test performance of HIV incidence determination was evaluated for 403 multi-assay algorithms [MAAs] that included the BED capture immunoassay [BED-CEIA] alone, an avidity assay alone, and combinations of these assays at different cutoff values with and without CD4 and viral load testing on samples from seven African cohorts (5,325 samples from 3,436 individuals with known duration of HIV infection [1 month to >10 years]). The mean window period (average time individuals appear positive for a given algorithm) and performance in estimating an incidence estimate (in terms of bias and variance) of these MAAs were evaluated in three simulated epidemic scenarios (stable, emerging and waning). The power of different test methods to detect a 35% reduction in incidence in the matched communities of Project Accept was also assessed. A MAA was identified that included BED-CEIA, the avidity assay, CD4 cell count, and viral load that had a window period of 259 days, accurately estimated HIV incidence in all three epidemic settings and provided sufficient power to detect an intervention effect in Project Accept. Conclusions In a Southern African setting, HIV incidence estimates and intervention effects can be accurately estimated from cross-sectional surveys using a MAA. The improved accuracy in cross-sectional incidence testing that a MAA provides is a powerful tool for HIV surveillance and program evaluation.

Development of a 16S rRNA gene-based prototype microarray for the detection of selected actinomycetes genera

Actinomycetes are known for their secondary metabolites, which have been successfully used as drugs in human and veterinary medicines. However, information on the distribution of this group of Gram-positive bacteria in diverse ecosystems and a comprehension of their activities in ecosystem processes are still scarce. We have developed a 16S rRNA-based taxonomic microarray that targets key actinomycetes at the genus level. In total, 113 actinomycete 16S rRNA probes, corresponding to 55 of the 202 described genera, were designed. The microarray accuracy was evaluated by comparing signal intensities with probe/target-weighted mismatch values and the Gibbs energy of the probe/target duplex formation by hybridizing 17 non-actinomycete and 29 actinomycete strains/clones with the probe set. The validation proved that the probe set was specific, with only 1.3% of false results. The incomplete coverage of actinomycetes by a genus-specific probe was caused by the limited number of 16S rRNA gene sequences in databases or insufficient 16S rRNA gene polymorphism. The microarray enabled discrimination between actinomycete communities from three forest soil samples collected at one site. Cloning and sequencing of 16S rRNA genes from one of the soil samples confirmed the microarray results. We propose that this newly constructed microarray will be a valuable tool for genus-level comparisons of actinomycete communities in various ecological conditions.

Actinobacterial community dominated by a distinct clade in acidic soil of a waterlogged deciduous forest

Members of the Actinobacteria are among the most important litter decomposers in soil. The site of a waterlogged deciduous forest with acidic soil was explored for actinobacteria because seasonality of litter inputs, temperature, and precipitation provided contrasting environmental conditions, particularly variation of organic matter quantity and quality. We hypothesized that these factors, which are known to influence decomposition, were also likely to affect actinobacterial community composition. The relationship between the actinobacterial community, soil moisture and organic matter content was assessed in two soil horizons in the summer and winter seasons using a 16S rRNA taxonomic microarray and cloning-sequencing of 16S rRNA genes. Both approaches showed that the community differed significantly between horizons and seasons, paralleling the changes in soil moisture and organic matter content. The microarray analysis further indicated that the actinobacterial community of the upper horizon was characterized by high incidence of the genus Mycobacterium. In both horizons and seasons, the actinobacterial clone libraries were dominated (by 80%) by sequences of a separate clade sharing an ancestral node with Streptosporangineae. This relatedness is supported also by some common adaptations, for example, to soil acidity and periodic oxygen deprivation or dryness.

Microbial Communities Show Parallels at Sites with Distinct Litter and Soil Characteristics

ABSTRACT Plant and microbial community composition in connection with soil chemistry determines soil nutrient cycling. The study aimed at demonstrating links between plant and microbial communities and soil chemistry occurring among and within four sites: two pine forests with contrasting soil pH and two grasslands of dissimilar soil chemistry and vegetation. Soil was characterized by C and N content, particle size, and profiles of low-molecular-weight compounds determined by high-performance liquid chromatography (HPLC) of soil extracts. Bacterial and actinobacterial community composition was assessed by terminal restriction fragment length polymorphism (T-RFLP) and cloning followed by sequencing. Abundances of bacteria, fungi, and actinobacteria were determined by quantitative PCR. In addition, a pool of secondary metabolites was estimated by erm resistance genes coding for rRNA methyltransferases. The sites were characterized by a stable proportion of C/N within each site, while on a larger scale, the grasslands had a significantly lower C/N ratio than the forests. A Spearmans test showed that soil pH was correlated with bacterial community composition not only among sites but also within each site. Bacterial, actinobacterial, and fungal abundances were related to carbon sources while T-RFLP-assessed microbial community composition was correlated with the chemical environment represented by HPLC profiles. Actinobacteria community composition was the only studied microbial characteristic correlated to all measured factors. It was concluded that the microbial communities of our sites were influenced primarily not only by soil abiotic characteristics but also by dominant litter quality, particularly, by percentage of recalcitrant compounds.

Determination of Factors Associated with Natural Soil Suppressivity to Potato Common Scab

Common scab of potatoes is a disease, which is difficult to manage due to complex interactions of the pathogenic bacteria (Streptomyces spp.) with soil, microbial community and potato plants. In Bohemian-Moravian Highlands in the Czech Republic two sites (Vyklantice and Zdirec) were selected for a study of common scab disease suppressivity. At both sites, a field with low disease severity occurs next to one with high severity and the situation was regularly observed over four decades although all four fields undergo a crop rotation. In the four fields, quantities of bacteria, actinobacteria and the gene txtB from the biosynthetic gene cluster of thaxtomin, the main pathogenicity factor of common scab, were analyzed by real-time PCR. Microbial community structure was compared by terminal fragment length polymorphism analysis. Soil and potato periderm were characterized by contents of carbon, nitrogen, phosporus, sulphur, calcium, magnesium, and iron. Quality of organic matter was assessed by high performance liquid chromatography of soil extracts. The study demonstrated that the suppressive character of the fields is locally specific. At Zdirec, the suppressivity was associated with low txtB gene copies in bulk soil, while at Vyklantice site it was associated with low txtB gene copies in the tuberosphere. The differences were discussed with respect to the effect of abiotic conditions at Zdirec and interaction between potato plant and soil microbial community at Vyklantice. Soil pH, Ca soil content or cation concentrations, although different were not in the range to predict the disease severity. Low severity of common scab was associated with low content of soil C, N, C/N, Ca and Fe suggesting that oligotrophic conditions may be favorable to common scab suppression.

Multivariate and functional covariates and conditional copulas

[Gijbels, Irene] Katholieke Univ Leuven, Dept Math, Louvain, Belgium. [Gijbels, Irene] Katholieke Univ Leuven, Leuven Stat Res Ctr LStat, Louvain, Belgium. [Omelka, Marek] Charles Univ Prague, Fac Math & Phys, Dept Probabil & Stat, Prague, Czech Republic. [Veraverbeke, Noel] Hasselt Univ, Ctr Stat, Hasselt, Belgium. [Veraverbeke, Noel] North West Univ, Unit BMI, Potchefstroom, South Africa. Irene.Gijbels@wis.kuleuven.be; omelka@karlin.mff.cuni.cz; noel.veraverbeke@uhasselt.be

Partial and average copulas and association measures

This research was supported by the IAP Research Network P7/06 of the Belgian State (Belgian Science Policy). The first author gratefully acknowledges support from the GOA/12/014 project of the Research Fund KU Leuven. The second author gratefully acknowledges support from the grant GACR 15-04774Y. The third author is an extraordinary professor at the North-West University, Potchefstroom, South Africa. The authors are grateful to an Associate Editor and two referees for their valuable comments that led to a considerable improvement of the paper.

Testing for Homogeneity of Multivariate Dispersions Using Dissimilarity Measures

Testing homogeneity of dispersions may be of its own scientific interest as well as an important auxiliary step verifying assumptions of a main analysis. The problem is that many biological and ecological data are highly skewed and zero-inflated. Also the number of variables often exceeds the sample size. Thus data analysts often do not rely on parametric assumptions, but use a particular dissimilarity measure to calculate a matrix of pairwise differences. This matrix is then the basis for further statistical inference. Anderson (2006) proposed a distance-based test of homogeneity of multivariate dispersions for a one-way ANOVA design, for which a matrix of pairwise dissimilarities can be taken as an input. The key idea, like in Levenes test, is to replace each observation with its distance to an estimated group center. In this paper we suggest an alternative approach that is based on the means of within-group distances and does not require group centre calculations to obtain the test statistic. We show that this approach can have theoretical as well as practical advantages. A permutation procedure that gives type I error close to the prescribed value even in small samples is described.