相关论文: On Stability and Decomposition of Sample Quantiles…

This paper studies an infinite horizon optimal control problem for discrete-time linear systems and quadratic criteria, both with random parameters which are independent and identically distributed with respect to time. A classical approach…

In this paper, we investigate the robust models for $\Lambda$-quantiles with partial information regarding the loss distribution, where $\Lambda$-quantiles extend the classical quantiles by replacing the fixed probability level with a…

Rate of convergence is studied for a diffusion process on the half line with a non-sticky reflection to a heavy-tailed 1D invariant distribution which density on the half line has a polynomial decay at infinity. Starting from a standard…

We develop a Quantile Bayesian Vector Autoregression (QBVAR) to forecast real oil prices across different quantiles of the conditional distribution. The model allows predictor effects to vary across quantiles, capturing asymmetries that…

For highly skewed or fat-tailed distributions, mean or median-based methods often fail to capture the central tendencies in the data. Despite being a viable alternative, estimating the conditional mode given certain covariates (or mode…

We use bias-reduced estimators of high quantiles, of heavy-tailed distributions, to introduce a new estimator of the mean in the case of infinite second moment. The asymptotic normality of the proposed estimator is established and checked,…

Datasets with extreme observations and/or heavy-tailed error distributions are commonly encountered and should be analyzed with careful consideration of these features from a statistical perspective. Small deviations from an assumed model,…

It has recently been shown that there are substantial differences in the regularity behavior of the empirical process based on scalar diffusions as compared to the classical empirical process, due to the existence of diffusion local time.…

Empirical-likelihood-based confidence intervals for a mean were introduced by Owen [Biometrika 75 (1988) 237-249], where at least a finite second moment is required. This excludes some important distributions, for example, those in the…

We focus on the construction of confidence corridors for multivariate nonparametric generalized quantile regression functions. This construction is based on asymptotic results for the maximal deviation between a suitable nonparametric…

We introduce the notion of symmetric covariation, which is a new measure of dependence between two components of a symmetric $\alpha$-stable random vector, where the stability parameter $\alpha$ measures the heavy-tailedness of its…

Estimating the structures at high or low quantiles has become an important subject and attracted increasing attention across numerous fields. However, due to data sparsity at tails, it usually is a challenging task to obtain reliable…

This paper focuses on generalizing quantiles from the ordering point of view. We propose the concept of partial quantiles, which are based on a given partial order. We establish that partial quantiles are equivariant under order-preserving…

We offer a survey of recent results on covariance estimation for heavy-tailed distributions. By unifying ideas scattered in the literature, we propose user-friendly methods that facilitate practical implementation. Specifically, we…

Linear quantile regression is a powerful tool to investigate how predictors may affect a response heterogeneously across different quantile levels. Unfortunately, existing approaches find it extremely difficult to adjust for any dependency…

In this work, we consider systems that are subjected to intermittent instabilities due to external stochastic excitation. These intermittent instabilities, though rare, have a large impact on the probabilistic response of the system and…

In this paper, we propose a distributionally robust safety verification method for Markov decision processes where only an ambiguous transition kernel is available instead of the precise transition kernel. We define the ambiguity set around…

A novel forecast combination and weighted quantile based tail-risk forecasting framework is proposed, aiming to reduce the impact of modelling uncertainty in tail-risk forecasting. The proposed approach is based on a two-step estimation…

In several different fields, there is interest in analyzing the upper or lower tail quantile of the underlying distribution rather than mean or center quantile. However, the investigation of the tail quantile is difficult because of data…

Motivated by applications in hydrodynamics and networks of thermostatically-control loads in buildings we study control of linear dynamical systems driven by additive and also multiplicative noise of a general position. Utilizing…