Projection Estimates of Constrained Functional Parameters

AMS classifications: 62G05; 62G07; 62G08; 62G20; 62G32;estimation;convex function;extreme value copula;Pickands dependence function;projection;shape constraint;support function;tangent cone

An M-Estimator for Tail Dependence in Arbitrary Dimensions

Consider a random sample in the max-domain of attraction of a multivariate extreme value distribution such that the dependence structure of the attractor belongs to a parametric model. A new estimator for the unknown parameter is defined as the value that minimises the distance between a vector of weighted integrals of the tail dependence function and their empirical counterparts. The minimisation problem has, with probability tending to one, a unique, global solution. The estimator is consistent and asymptotically normal. The spectral measures of the tail dependence models to which the method applies can be discrete or continuous. Examples demonstrate the applicability and the performance of the method.asymptotic statistics;factor model;M-estimation;multivariate extremes;tail dependence

Inference on the tail process with application to financial time series modelling

To draw inference on serial extremal dependence within heavy-tailed Markov chains, Drees, Segers and Warcho{\l} [Extremes (2015) 18, 369--402] proposed nonparametric estimators of the spectral tail process. The methodology can be extended to the more general setting of a stationary, regularly varying time series. The large-sample distribution of the estimators is derived via empirical process theory for cluster functionals. The finite-sample performance of these estimators is evaluated via Monte Carlo simulations. Moreover, two different bootstrap schemes are employed which yield confidence intervals for the pre-asymptotic spectral tail process: the stationary bootstrap and the multiplier block bootstrap. The estimators are applied to stock price data to study the persistence of positive and negative shocks.Comment: 22 page

Multivariate Nonparametric Estimation of the Pickands Dependence Function using Bernstein Polynomials

Many applications in risk analysis, especially in environmental sciences, require the estimation of the dependence among multivariate maxima. A way to do this is by inferring the Pickands dependence function of the underlying extreme-value copula. A nonparametric estimator is constructed as the sample equivalent of a multivariate extension of the madogram. Shape constraints on the family of Pickands dependence functions are taken into account by means of a representation in terms of a specific type of Bernstein polynomials. The large-sample theory of the estimator is developed and its finite-sample performance is evaluated with a simulation study. The approach is illustrated by analyzing clusters consisting of seven weather stations that have recorded weekly maxima of hourly rainfall in France from 1993 to 2011

Projection Estimates of Constrained Functional Parameters

AMS classifications: 62G05; 62G07; 62G08; 62G20; 62G32;

Validation of IFE-1.6 SCIAMACHY limb ozone profiles

International audienceThe IFE-1.6 scientific data set of SCIAMACHY limb ozone profiles is validated for the period August?December 2002. The data set provides ozone profiles over an altitude range of 15?45 km. The main uncertainty in the profiles is the imprecise knowledge of the pointing of the instrument, leading to retrieved profiles that are shifted in altitude direction. To obtain a first order correction for the pointing error and the remaining uncertainties, the retrieved profiles are compared to their a-priori value and ozone sondes based on absolute distance and equivalent latitude criteria. A vertical shift of the satellite profiles with 2 km downward is found to be an appropriate correction for the data set studied. A total root-mean-square difference between limb profiles and sondes of 10?15% remains for the stratospheric ozone profile after application of the correction. Small biases are left above and below the ozone maximum at mid latitudes, where the vertical gradients in the retrieved product are in general too strong

Aging is associated with an earlier arrival of reflected waves without a distal shift in reflection sites

Background-Despite pronounced increases in central pulse wave velocity (PWV) with aging, reflected wave transit time (RWTT), traditionally defined as the timing of the inflection point (T-INF) in the central pressure waveform, does not appreciably decrease, leading to the controversial proposition of a "distal-shift" of reflection sites. T-INF, however, is exceptionally prone to measurement error and is also affected by ejection pattern and not only by wave reflection. We assessed whether RWTT, assessed by advanced pressure-flow analysis, demonstrates the expected decline with aging. Methods and Results-We studied a sample of unselected adults without cardiovascular disease (n=48; median age 48 years) and a clinical population of older adults with suspected/established cardiovascular disease (n=164; 61 years). We measured central pressure and flow with carotid tonometry and phase-contrast MRI, respectively. We assessed RWTT using wave-separation analysis (RWTTWSA) and partially distributed tube-load (TL) modeling (RWTTTL). Consistent with previous reports, T-INF did not appreciably decrease with age despite pronounced increases in PWV in both populations. However, aging was associated with pronounced decreases in RWTTWSA (general population -15.0 ms/decade, P<0.001; clinical population -9.07 ms/decade, P=0.003) and RWTTTL (general -15.8 ms/decade, P<0.001; clinical -11.8 ms/decade, P<0.001). There was no evidence of an increased effective reflecting distance by either method. TINF was shown to reliably represent RWTT only under highly unrealistic assumptions about input impedance. Conclusions-RWTT declines with age in parallel with increased PWV, with earlier effects of wave reflections and without a distal shift in reflecting sites. These findings have important implications for our understanding of the role of wave reflections with aging