arXiv research

This paper strengthens the central limit theorem for order statistics using relative entropy.

This paper simplifies computing higher-order $U$-statistics efficiently.

The paper provides bounds for high-dimensional U-statistics with novel order-explicit inequalities.

TSCD is an algorithm for causal discovery using second-order statistics.

Model uses statistical physics principles to predict financial market volatility and returns.

New method combines score lists using joint CDFs, improving computation.

New estimator stabilizes higher-order influence functions for stable statistical inference.

Paper proposes efficient methods for high-order clustering in tensor block models.

While records and order statistics of independent and identically distributed (i.i.d.) random variables X_1, ..., X_N are fully understood, much less is known for strongly correlated random variables, which is often the situation encountered in statistical physics. Recently, it was shown, in a series of works, that one…

New quantum states capture more information, enabling advanced processing tasks.

Ordinal regression falls between discrete-valued classification and continuous-valued regression. Ordinal target variables can be associated with ranked random variables. These random variables are known as order statistics and they are closely related to ordinal regression. However, the challenge of using order statis…

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

Improved computational complexity in statistical models using second-order information.

New estimator stabilizes higher-order influence functions for bilinear forms.

We develop a new statistical test for comparing variables with varying scales.

Statistical shape models enhance machine learning algorithms providing prior information about deformation. A Point Distribution Model (PDM) is a popular landmark-based statistical shape model for segmentation. It requires choosing a model order, which determines how much of the variation seen in the training data is a…

Diffusion models learn simple statistics before complex ones, revealing a sample complexity exponent.

Study improves BN TTA under distribution shift using higher-order asymptotics.

Finding statistically significant high-order interaction features in predictive modeling is important but challenging task. The difficulty lies in the fact that, for a recent applications with high-dimensional covariates, the number of possible high-order interaction features would be extremely large. Identifying stati…

New tests detect high-order interactions without permutations.

Paper explores limits of high-order clustering with planted structures.

Neural networks can learn from higher-order cumulants efficiently, requiring quadratic samples.

New stable HOIF estimators for statistical functionals.

New method finds significant high-order interactions efficiently.

New statistical models for predicting ranked preferences from partial orders.

The purpose of this paper is to provide a sharp analysis on the asymptotic behavior of the Durbin-Watson statistic. We focus our attention on the first-order autoregressive process where the driven noise is also given by a first-order autoregressive process. We establish the almost sure convergence and the asymptotic n…

The paper reviews recent statistical methods for financial markets, focusing on jumps, volatility, and microstructure noise.

Improved estimation of higher order integrals using shrinkage techniques.

New method for zeroth-order stochastic gradient algorithms provides confidence intervals.

We propose a model for price formation in financial markets based on clearing of a standard call auction with random orders, and verify its validity for prediction of the daily closing price distribution statistically. The model considers random buy and sell orders, placed following demand- and supply-side valuation di…

We present an extension of the Kolmogorov-Smirnov (KS) two-sample test, which can be more sensitive to differences in the tails. Our test statistic is an integral probability metric (IPM) defined over a higher-order total variation ball, recovering the original KS test as its simplest case. We give an exact representer…

Study quantifies how LLMs capture higher-order statistical structure using cumulant expansion.

A new model predicts race places using changeover-times and log-normal distributions.

Unified geometric interpretation of statistical estimation inequalities.

A new method for faster optimization on statistical manifolds.

Improved simulation of phase transitions using hierarchical autoregressive networks.

New method uses statistical physics to detect financial market manipulation.

New inequalities help optimize first-order algorithms for statistical risk analysis.

In this study, we analyze the aerospace stocks prices in order to characterize the sector behavior. The data analyzed cover the period from January 1987 to April 1999. We present a new index for the aerospace sector and we investigate the statistical characteristics of this index. Our results show that this index is we…

Estimates hypergraphons for modeling complex interactions efficiently.

We develop a theory of higher-order feature attribution for complex models.

Flexible approach for normal approximations in geometric and topological statistics.

New theory allows ICA without assuming non-Gaussian sources.

We show that the statistics of spreads in real order books is characterized by an intrinsic asymmetry due to discreteness effects for even or odd values of the spread. An analysis of data from the NYSE order book points out that traders' strategies contribute to this asymmetry. We also investigate this phenomenon in th…

This work proposes a model for geodesic distances and flows on manifolds.

This article develops a statistical test for the null hypothesis of strict stationarity of a discrete time stochastic process in the frequency domain. When the null hypothesis is true, the second order cumulant spectrum is zero at all the discrete Fourier frequency pairs in the principal domain. The test uses a window …

LOB-Bench benchmarks generative AI for financial data, outperforming traditional models.

Bayesian method reconstructs hidden higher-order interactions from network data.