Of copulas, quantiles, ranks and spectra: An L1L_1-approach to spectral analysis

In this paper, we present an alternative method for the spectral analysis of a univariate, strictly stationary time series $\{Y_t\}_{t\in \mathbb {Z}}$. We define a "new" spectrum as the Fourier transform of the differences between copulas of the pairs $(Y_t,Y_{t-k})$ and the independence copula. This object is called a copula spectral density kernel and allows to separate the marginal and serial aspects of a time series. We show that this spectrum is closely related to the concept of quantile regression. Like quantile regression, which provides much more information about conditional distributions than classical location-scale regression models, copula spectral density kernels are more informative than traditional spectral densities obtained from classical autocovariances. In particular, copula spectral density kernels, in their population versions, provide (asymptotically provide, in their sample versions) a complete description of the copulas of all pairs $(Y_t,Y_{t-k})$. Moreover, they inherit the robustness properties of classical quantile regression, and do not require any distributional assumptions such as the existence of finite moments. In order to estimate the copula spectral density kernel, we introduce rank-based Laplace periodograms which are calculated as bilinear forms of weighted $L_1$-projections of the ranks of the observed time series onto a harmonic regression model. We establish the asymptotic distribution of those periodograms, and the consistency of adequately smoothed versions. The finite-sample properties of the new methodology, and its potential for applications are briefly investigated by simulations and a short empirical example.Comment: Published at http://dx.doi.org/10.3150/13-BEJ587 in the Bernoulli (http://isi.cbs.nl/bernoulli/) by the International Statistical Institute/Bernoulli Society (http://isi.cbs.nl/BS/bshome.htm

Phylogenetic Analysis of Staphylococcus aureus CC398 Reveals a Sub-Lineage Epidemiologically Associated with Infections in Horses

In the early 2000s, a particular MRSA clonal complex (CC398) was found mainly in pigs and pig farmers in Europe. Since then, CC398 has been detected among a wide variety of animal species worldwide. We investigated the population structure of CC398 through mutation discovery at 97 genetic housekeeping loci, which are distributed along the CC398 chromosome within 195 CC398 isolates, collected from various countries and host species, including humans. Most of the isolates in this collection were received from collaborating microbiologists, who had preserved them over years. We discovered 96 bi-allelic polymorphisms, and phylogenetic analyses revealed that an epidemic sub-clone within CC398 (dubbed 'clade (C)') has spread within and between equine hospitals, where it causes nosocomial infections in horses and colonises the personnel. While clade (C) was strongly associated with S. aureus from horses in veterinary-care settings (p = 2 × 10(-7)), it remained extremely rare among S. aureus isolates from human infections

2013/30 On Hodges and Lehman's "6/pi Result"

While the asymptotic relative efficiency (ARE) of Wilcoxon rank-based tests for location and regression with respect to their parametric Student competitors can be arbitrarily large, Hodges and Lehmann (1961) have shown that the ARE of the same Wilcoxon tests with respect to their van der Waerden or normal-score counterparts is bounded from above by 6/π ≈ 1.910. In this paper, we revisit that result, and investigate similar bounds for statistics based on Student scores. We also consider the serial version of this ARE. More precisely, we study the ARE, under various densities, of the Spearman-Wald-Wolfowitz and Kendall rank-based autocorrelations with respect to the van der Waerden or normal-score ones used to test (ARMA) serial dependence alternatives

Kernel density estimation on random fields: the L1 theory

Kernel-type estimators of the multivariate density of stationary random fields indexed by multidimensional lattice points space are investigated. Sufficient conditions for kernel estimators to converge in L1 are obtained. The results are applicable to a large class of spatial processes.info:eu-repo/semantics/publishe