Confidence regions for high quantiles of a heavy tailed distribution

Estimating high quantiles plays an important role in the context of risk management. This involves extrapolation of an unknown distribution function. In this paper we propose three methods, namely, the normal approximation method, the likelihood ratio method and the data tilting method, to construct confidence regions for high quantiles of a heavy tailed distribution. A simulation study prefers the data tilting method.Comment: Published at http://dx.doi.org/10.1214/009053606000000416 in the Annals of Statistics (http://www.imstat.org/aos/) by the Institute of Mathematical Statistics (http://www.imstat.org

Reduce computation in profile empirical likelihood method

Since its introduction by Owen in [29, 30], the empirical likelihood method has been extensively investigated and widely used to construct confidence regions and to test hypotheses in the literature. For a large class of statistics that can be obtained via solving estimating equations, the empirical likelihood function can be formulated from these estimating equations as proposed by [35]. If only a small part of parameters is of interest, a profile empirical likelihood method has to be employed to construct confidence regions, which could be computationally costly. In this paper we propose a jackknife empirical likelihood method to overcome this computational burden. This proposed method is easy to implement and works well in practice.profile empirical likelihood; estimating equation; Jackknife

Investigation on inlet and entry region characteristics on the discrete passage diffuser pressure rise performance

Thesis (M.S.)--Massachusetts Institute of Technology, Dept. of Aeronautics and Astronautics, 1994.Includes bibliographical references (p. 65-67).by Yongcheng Liang.M.S

Bootstrap approximation of tail dependence function

Abstract For estimating a rare event via the multivariate extreme value theory, the so-called tail dependence function has to be investigated (see [L. . In this paper, we first derive a bootstrap approximation for a tail dependence function with an approximation rate via the construction approach developed by [K. Chen, S.H. Lo, On a mapping approach to investigating the bootstrap accuracy, Probab. Theory Relat. Fields 107 (1997) 197-217], and then apply it to construct a confidence band for the tail dependence function. A simulation study is conducted to assess the accuracy of the bootstrap approach

Theoretical Evidence for the Berry-Phase Mechanism of Anomalous Hall Transport: First-principles Studies on CuCr2_2Se4−x_{4-x}Brx_x

To justify the origin of anomalous Hall effect (AHE), it is highly desirable to have the system parameters tuned continuously. By quantitative calculations, we show that the doping dependent sign reversal in CuCr$_{2}$Se$_{4-x}$Br$_{x}$, observed but not understood, is nothing but direct evidence for the Berry-Phase mechanism of AHE. The systematic calculations well explain the experiment data for the whole doping range where the impurity scattering rates is changed by several orders with Br substitution. Further sign change is also predicted, which may be tested by future experiments.Comment: 4 page

Report of the Topical Group on Electroweak Precision Physics and Constraining New Physics for Snowmass 2021

The precise measurement of physics observables and the test of their consistency within the standard model (SM) are an invaluable approach, complemented by direct searches for new particles, to determine the existence of physics beyond the standard model (BSM). Studies of massive electroweak gauge bosons (W and Z bosons) are a promising target for indirect BSM searches, since the interactions of photons and gluons are strongly constrained by the unbroken gauge symmetries. They can be divided into two categories: (a) Fermion scattering processes mediated by s- or t-channel W/Z bosons, also known as electroweak precision measurements; and (b) multi-boson processes, which include production of two or more vector bosons in fermion-antifermion annihilation, as well as vector boson scattering (VBS) processes. The latter categories can test modifications of gauge-boson self-interactions, and the sensitivity is typically improved with increased collision energy. This report evaluates the achievable precision of a range of future experiments, which depend on the statistics of the collected data sample, the experimental and theoretical systematic uncertainties, and their correlations. In addition it presents a combined interpretation of these results, together with similar studies in the Higgs and top sector, in the Standard Model effective field theory (SMEFT) framework. This framework provides a model-independent prescription to put generic constraints on new physics and to study and combine large sets of experimental observables, assuming that the new physics scales are significantly higher than the EW scale.Comment: 55 pages; Report of the EF04 topical group for Snowmass 202