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Quantiles and expected shortfalls are commonly used risk measures in financial risk management. The two measurements are correlated while having distinguished features. In this project, our primary goal is to develop a stable and practical inference method for the conditional expected shortfall. We consider the joint modelling of conditional quantile and expected shortfall to facilitate the statistical inference procedure. While the regression coefficients can be estimated jointly by minimizing a class of strictly consistent joint loss functions, the computation is challenging, especially when the dimension of parameters is large since the loss functions are neither differentiable nor convex. We propose a two‐step estimation procedure to reduce the computational effort by first estimating the quantile regression parameters with standard quantile regression. We show that the two‐step estimator has the same asymptotic properties as the joint estimator, but the former is numerically more efficient. We develop a score‐type inference method for hypothesis testing and confidence interval construction. Compared to the Wald‐type method, the score method is robust against heterogeneity and is superior in finite samples, especially for cases with many confounding factors. The advantages of our proposed method over existing approaches are demonstrated by simulations and empirical studies based on income and college education data.

 

Abstract Ultralight bosons such as axion-like particles are viable candidates for dark matter. They can form stable, macroscopic field configurations in the form of topological defects that could concentrate the dark matter density into many distinct, compact spatial regions that are small compared with the Galaxy but much larger than the Earth. Here we report the results of the search for transient signals from the domain walls of axion-like particles by using the global network of optical magnetometers for exotic (GNOME) physics searches. We search the data, consisting of correlated measurements from optical atomic magnetometers located in laboratories all over the world, for patterns of signals propagating through the network consistent with domain walls. The analysis of these data from a continuous month-long operation of GNOME finds no statistically significant signals, thus placing experimental constraints on such dark matter scenarios. 

Numerous observations suggest that there exist undiscovered beyond‐the‐standard‐model particles and fields. Because of their unknown nature, these exotic particles and fields could interact with standard model particles in many different ways and assume a variety of possible configurations. Here, an overview of the global network of optical magnetometers for exotic physics searches (GNOME), the ongoing experimental program designed to test a wide range of exotic physics scenarios, is presented. The GNOME experiment utilizes a worldwide network of shielded atomic magnetometers (and, more recently, comagnetometers) to search for spatially and temporally correlated signals due to torques on atomic spins from exotic fields of astrophysical origin. The temporal characteristics of a variety of possible signals currently under investigation such as those from topological defect dark matter (axion‐like particle domain walls), axion‐like particle stars, solitons of complex‐valued scalar fields (Q‐balls), stochastic fluctuations of bosonic dark matter fields, a solar axion‐like particle halo, and bursts of ultralight bosonic fields produced by cataclysmic astrophysical events such as binary black hole mergers are surveyed.