The behavior of locally most powerful tests

summary:The locally most powerful (LMP) tests of the hypothesis $H: \theta =\theta _0$ against one-sided as well as two-sided alternatives are compared with several competitive tests, as the likelihood ratio tests, the Wald-type tests and the Rao score tests, for several distribution shapes and for location, shape and vector parameters. A simulation study confirms the importance of the condition of local unbiasedness of the test, and shows that the LMP test can sometimes dominate the other tests only in a very restricted neighborhood of $H.$ Hence, we cannot recommend a universal application of the LMP tests in practice. The tests with a high Bahadur efficiency, though not exactly LMP, also seem to be good in the local sense

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, Radulovi\v{c} 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 corner 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, Radulovi\v{c} 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.Comment: Published in at http://dx.doi.org/10.1214/08-AOS666 the Annals of Statistics (http://www.imstat.org/aos/) by the Institute of Mathematical Statistics (http://www.imstat.org

Generalized Hadamard differentiability of the copula mapping and its applications

We consider the copula mapping, which maps a joint cumulative distribution function to the corresponding copula. Its Hadamard differentiablity was shown in van der Vaart and Wellner (1996), Fermanian et al. (2004) and (under less strict assumptions) in B\"ucher and Volgushev (2013). This differentiability result has proved to be a powerful tool to show weak convergence of empirical copula processes in various settings using the functional delta method. We state a generalization of the Hadamard differentiability results that simplifies the derivations of asymptotic expansions and weak convergence of empirical copula processes in the presence of covariates. The usefulness of this result is illustrated on several applications which include a multidimensional functional linear model, where the copula of the error vector describes the dependency between the components of the vector of observations, given the functional covariate.Comment: 34 page

Nonparametic Estimation of Copulas, Conditional Copulas and Conditional Distribution Function

Matematicko-fyzikální fakult

A Short-Term Response of Soil Microbial Communities to Cadmium and Organic Substrate Amendment in Long-Term Contaminated Soil by Toxic Elements

Two long-term contaminated soils differing in contents of Pb, Zn, As, Cd were compared in a microcosm experiment for changes in microbial community structure and respiration after various treatments. We observed that the extent of long-term contamination (over 200 years) by toxic elements did not change the total numbers and diversity of bacteria but influenced their community composition. Namely, numbers of Actinobacteria determined by phylum specific qPCR increased and also the proportion of Actinobacteria and Chloroflexi increased in Illumina sequence libraries in the more contaminated soil. In the experiment, secondary disturbance by supplemented cadmium (doses from double to 100-fold the concentration in the original soil) and organic substrates (cellobiose or straw) increased bacterial diversity in the less contaminated soil and decreased it in the more contaminated soil. Respiration in the experiment was higher in the more contaminated soil in all treatments and correlated with bacterial numbers. Considering the most significant changes in bacterial community, it seemed that particularly Actinobacteria withstand contamination by toxic elements. The results proved higher resistance to secondary disturbance in terms of both, respiration and bacterial community structure in the less contaminated soil

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

DNA conformations and their sequence preferences

The geometry of the phosphodiester backbone was analyzed for 7739 dinucleotides from 447 selected crystal structures of naked and complexed DNA. Ten torsion angles of a near-dinucleotide unit have been studied by combining Fourier averaging and clustering. Besides the known variants of the A-, B- and Z-DNA forms, we have also identified combined A + B backbone-deformed conformers, e.g. with α/γ switches, and a few conformers with a syn orientation of bases occurring e.g. in G-quadruplex structures. A plethora of A- and B-like conformers show a close relationship between the A- and B-form double helices. A comparison of the populations of the conformers occurring in naked and complexed DNA has revealed a significant broadening of the DNA conformational space in the complexes, but the conformers still remain within the limits defined by the A- and B- forms. Possible sequence preferences, important for sequence-dependent recognition, have been assessed for the main A and B conformers by means of statistical goodness-of-fit tests. The structural properties of the backbone in quadruplexes, junctions and histone-core particles are discussed in further detail

Asymptotické vlastnosti druhého řádu některých M-odhadů a R-odhadů

Katedra pravděpodobnosti a matematické statistikyDepartment of Probability and Mathematical StatisticsFaculty of Mathematics and PhysicsMatematicko-fyzikální fakult