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

We introduce a robust estimator of the location parameter for the change-point in the mean based on the Wilcoxon statistic and establish its consistency for $L_1$ near epoch dependent processes. It is shown that the consistency rate depends…

We propose a novel, succinct, and effective approach for distribution prediction to quantify uncertainty in machine learning. It incorporates adaptively flexible distribution prediction of $\mathbb{P}(\mathbf{y}|\mathbf{X}=x)$ in regression…

The weak convergence of the quantile processes, which are constructed based on different estimators of the finite population quantiles, is shown under various well-known sampling designs based on a superpopulation model. The results related…

In risk management, tail risks are of crucial importance. The assessment of risks should be carried out in accordance with the regulatory authority's requirement at high quantiles. In general, the underlying distribution function is…

The performance of quantum key distribution (QKD) heavily depends on statistical inference. For a broad class of protocols, the central statistical task is a random sampling problem, customarily addressed using a hypergeometric tail bound…

Addendum: The generalized Box-M\"uller algorithm provides a methodology for generating q-Gaussian random variates. The parameter $-\infty<q\leq3$ is related to the shape of the tail decay; $q<1$ for compact-support including parabola…

Distribution estimation for noisy data via density deconvolution is a notoriously difficult problem for typical noise distributions like Gaussian. We develop a density deconvolution estimator based on quadratic programming (QP) that can…

Using an intrinsic approach, we study some properties of random fields which appear as tail fields of regularly varying stationary random fields. The index set is allowed to be a general locally compact Hausdorff Abelian group $\mathbb{G}$.…

We introduce $\zeta$- and $s$-values as quantile-based standardizations that are particularly suited for hypothesis testing. Unlike p-values, which express tail probabilities, $s$-values measure the number of semi-tail units into a…

Quantile regression is a powerful tool for learning the relationship between a response variable and a multivariate predictor while exploring heterogeneous effects. In this paper, we consider statistical inference for quantile regression…

Quantile regression has demonstrated promising utility in longitudinal data analysis. Existing work is primarily focused on modeling cross-sectional outcomes, while outcome trajectories often carry more substantive information in practice.…

(The third edition corrects minor typos and adds 3 chapters synthesized from published papers plus an appendix on maximum entropy distributions.) The monograph investigates the misapplication of conventional statistical techniques to fat…

Our aim is to study the backward problem, i.e. recover the initial data from the terminal observation, of the subdiffusion with time dependent coefficients. First of all, by using the smoothing property of solution operators and a…

Quantifying the impact of parametric and model-form uncertainty on the predictions of stochastic models is a key challenge in many applications. Previous work has shown that the relative entropy rate is an effective tool for deriving…

This paper develops robust inference methods for predictive regressions that address key challenges posed by endogenously persistent or heavy-tailed regressors, as well as persistent volatility in errors. Building on the Cauchy estimation…

In this paper, we introduce quantile coherency to measure general dependence structures emerging in the joint distribution in the frequency domain and argue that this type of dependence is natural for economic time series but remains…

By introducing a weight function into the density power divergence, we develop a new class of robust and smooth estimators for the tail index of Pareto-type distributions, offering improved efficiency in the presence of outliers. These…

I report a new statistical distribution formulated to confront the infamous, long-standing, computational/modeling challenge presented by highly skewed and/or leptokurtic ("fat- or heavy-tailed") data. The distribution is straightforward,…

Common statistical measures of uncertainty such as $p$-values and confidence intervals quantify the uncertainty due to sampling, that is, the uncertainty due to not observing the full population. However, sampling is not the only source of…

We obtain an uniform tail estimates for natural normed sums of independent random variables (r.v.) with regular varying tails of distributions. We give also many examples on order to show the exactness of offered estimates and discuss some…