arXiv research

Study on U-statistics with heavy-tailed samples, providing tail bounds and LDP.

The book chapter discusses tail risk analysis for financial data using extreme value statistics.

The paper studies quantile contributions and their relationship with order statistics in heavy-tailed distributions.

HTFM improves mode coverage and tail-statistic recovery for heavy-tailed data.

New algorithm improves heavy-tailed statistical estimation in streaming data.

Heavy-tailed outliers are more resilient to robust estimation than adversarial ones.

Study shows heavy-tailed distributions affect reliability of machine learning calibration statistics.

A new algebra for probabilistic programming improves tail behavior accuracy.

This work extends diffusion models to handle heavy-tailed targets, improving score estimation and sampling guarantees.

We analyze the statistical dependency structure of the S&P 500 constituents in the 4-year period from 2007 to 2010 using intraday data from the New York Stock Exchange's TAQ database. With a copula-based approach, we find that the statistical dependencies are very strong in the tails of the marginal distributions. This…

We introduce a new statistical tool (the TP-statistic and TE-statistic) designed specifically to compare the behavior of the sample tail of distributions with power-law and exponential tails as a function of the lower threshold u. One important property of these statistics is that they converge to zero for power laws o…

Paper presents a dynamic tail risk protection strategy using ML and econometrics.

Improved Clipped-SGD achieves near-optimal heavy-tailed statistical estimation in streaming settings.

The paper explores tail diversification in financial markets using entropy and mutual information.

Paper quantizes heavy-tailed data for near optimal estimation rates.

Extreme value theory enhances statistical learning extrapolation for rare events.

Paper develops robust policy evaluation for reinforcement learning with outlier and heavy-tailed rewards.

Paper examines the structure of stochastic gradients in deep learning.

Efficiently estimates sparse mean from heavy-tailed data.

In complex systems such as turbulent flows and financial markets, the dynamics in long and short time-lags, signaled by Gaussian and fat-tailed statistics, respectively, calls for a unified description. To address this issue we analyze a real dataset, namely, price fluctuations, in a wide range of temporal scales to em…

Deep models can't generate heavy-tailed samples well.

New theory predicts deep neural networks can operate in an extended critical regime without fine-tuning.

Financial time series have been investigated to follow fat-tailed distributions. Further, an empirical probability distribution sometimes shows cut-off shapes on its tails. To describe this stylized fact, we incorporate the cut-off effect in superstatistics. Then we confirm that the presented stochastic model is capabl…

We improve generative models for heavy-tailed multivariate data using an invariant statistical loss.

Survey of robust statistical methods for efficient computation.

The 20/60/20 rule improves risk management and portfolio optimization in finance.

This paper improves the robustness of risk estimation for financial positions.

Concentration inequalities form an essential toolkit in the study of high dimensional (HD) statistical methods. Most of the relevant statistics literature in this regard is based on sub-Gaussian or sub-exponential tail assumptions. In this paper, we first bring together various probabilistic inequalities for sums of in…

Paper proposes a 1-bit quantization scheme for high-dimensional statistical estimation.

A federated learning framework using superquantile aggregation for robust performance across heterogeneous data.

A new algorithm improves both computational efficiency and statistical optimality for robust low-rank matrix and tensor estimation.

Exponential Lasso improves Lasso's robustness to outliers and heavy-tailed noise.

In this paper we introduce an efficient fat-tail measurement framework that is based on the conditional second moments. We construct a goodness-of-fit statistic that has a direct interpretation and can be used to assess the impact of fat-tails on central data conditional dispersion. Next, we show how to use this framew…

This paper attempts to provide a decision-theoretic foundation for the measurement of economic tail risk, which is not only closely related to utility theory but also relevant to statistical model uncertainty. The main result is that the only risk measures that satisfy a set of economic axioms for the Choquet expected …

Paper proposes robust estimators for heavy-tailed data with infinite variance.

Paper establishes identifiability and elicitability of tail risk measures.

This study empirically re-examines fat tails in stock return distributions by applying statistical methods to an extensive dataset taken from the Korean stock market. The tails of the return distributions are shown to be much fatter in recent periods than in past periods and much fatter for small-capitalization stocks …

This work achieves exponential concentration in heavy-tailed data over CAT(κ) spaces using the Fréchet median.

Study on estimating rank-one tensors in noisy data with heavy tails.

Framework ensures alignment between humans and machines in LLMs.

This paper assesses tail risk and systemic risk in cryptocurrencies using expectiles and MES.

PPO's gradients are heavy-tailed, affecting learning; a robust estimator improves performance.

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 unknown, the database is sparse, and therefore special tail models are used. Very often…

Introduces Polar Depth for analyzing multivariate heavy-tailed data extremes.

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, flexible and effective. Even when working with far fewer data points than are rou…

Using the framework of factor models, we establish the general expression of the coefficient of tail dependence between the market and a stock (i.e., the probability that the stock incurs a large loss, assuming that the market has also undergone a large loss) as a function of the parameters of the underlying factor mod…

We survey some of the recent advances in mean estimation and regression function estimation. In particular, we describe sub-Gaussian mean estimators for possibly heavy-tailed data both in the univariate and multivariate settings. We focus on estimators based on median-of-means techniques but other methods such as the t…

This study uses local Gaussian correlation to analyze stock return tails, revealing more sensitive network properties.