arXiv research

The paper classifies and computes limits of equivariant compactifications of groups.

Meta two-sample testing uses auxiliary data to quickly find powerful tests from limited samples.

This work presents a theoretical and empirical evaluation of Anderson-Darling test when the sample size is limited. The test can be applied in order to backtest the risk factors dynamics in the context of Counterparty Credit Risk modelling. We show the limits of such test when backtesting the distributions of an intere…

Testing independence is of significant interest in many important areas of large-scale inference. Using extreme-value form statistics to test against sparse alternatives and using quadratic form statistics to test against dense alternatives are two important testing procedures for high-dimensional independence. However…

In this paper, we build tests for the presence of residual noise in a model where the market microstructure noise is a known parametric function of some variables from the limit order book. The tests compare two distinct quasi-maximum likelihood estimators of volatility, where the related model includes a residual nois…

New framework limits testing algorithmic stability under computational constraints.

The statistical analysis of discrete data has been the subject of extensive statistical research dating back to the work of Pearson. In this survey we review some recently developed methods for testing hypotheses about high-dimensional multinomials. Traditional tests like the $χ^2$ test and the likelihood ratio test ca…

New method tests conditional independence using spectral representations.

High-dimensional U-statistics show surprising phase transitions, impacting kernel-based tests.

New tests detect high-order interactions without permutations.

Given a polarized complex manifold, projection of a torus-equivariant test configuration to holomorphic vector fields was introduced by G. Székelyhidi, as the limit of the associated $\mathbb{C}^*$-actions. We show that there actually holds the moment convergence of the weight distributions. Our analytic approach at th…

Study phase transitions in identifying infected individuals using group testing.

MMD test detects adversarial attacks by addressing kernel limitations and non-independence issues.

Kernel tests assess equivalence between distributions without assuming specific moments.

In this paper, we consider a framework adapting the notion of cointegration when two asset prices are generated by a driftless Itô-semimartingale featuring jumps with infinite activity, observed regularly and synchronously at high frequency. We develop a regression based estimation of the cointegrated relations method …

The study connects K-stability and large complex structure limits in mirror symmetry.

Derives ideal train/test split for ridge regression in large data limit.

A new test statistic speeds up MMD while maintaining power.

Infinitesimal boosting converges to a deterministic process in large sample limit.

Tests if vertices in graphs have the same latent positions.

Discusses MultiFIT for multivariate dependence, comparing it to HSIC tests.

Study sets limits for detecting a subhypergraph in uniform hypergraphs.

Develops CLTs for Markov chain transition probabilities and policies.

Subjective expected utility theory assumes that decision-makers possess unlimited computational resources to reason about their choices; however, virtually all decisions in everyday life are made under resource constraints - i.e. decision-makers are bounded in their rationality. Here we experimentally tested the predic…

We develop a pivotal test to assess the statistical significance of the feature variables in a single-layer feedforward neural network regression model. We propose a gradient-based test statistic and study its asymptotics using nonparametric techniques. Under technical conditions, the limiting distribution is given by …

New methods cluster and test graphs without vertex correspondence.

Survey on statistical inference under memory constraints.

The paper improves confidence intervals for test error using cross-validation.

We propose procedures for testing whether stock price processes are martingales based on limit order type betting strategies. We first show that the null hypothesis of martingale property of a stock price process can be tested based on the capital process of a betting strategy. In particular with high frequency Markov …

In this paper we consider a Lagrange Multiplier-type test (LM) to detect change in the mean of time series with heteroskedasticity of unknown form. We derive the limiting distribution under the null, and prove the consistency of the test against the alternative of either an abrupt or smooth changes in the mean. We perf…

Hypothesis testing for graphs has been an important tool in applied research fields for more than two decades, and still remains a challenging problem as one often needs to draw inference from few replicates of large graphs. Recent studies in statistics and learning theory have provided some theoretical insights about …

Paper proposes an intelligent credit limit management system using causal inference.

We study the analytical properties of a one-side order book model in which the flows of limit and market orders are Poisson processes and the distribution of lifetimes of cancelled orders is exponential. Although simplistic, the model provides an analytical tractability that should not be overlooked. Using basic result…

Accurate goodness-of-fit tests for the extreme tails of empirical distributions is a very important issue, relevant in many contexts, including geophysics, insurance, and finance. We have derived exact asymptotic results for a generalization of the large-sample Kolmogorov-Smirnov test, well suited to testing these extr…

The paper explores statistical limits for detecting correlation in tree structures.

This paper explores two classes of model adaptation methods for Web search ranking: Model Interpolation and error-driven learning approaches based on a boosting algorithm. The results show that model interpolation, though simple, achieves the best results on all the open test sets where the test data is very different …

Best-of-$\infty$ improves LLM performance by efficiently allocating inference-time computation.

The theory of acceptance sets and their associated risk measures plays a key role in the design of capital adequacy tests. The objective of this paper is to investigate, in the context of bounded financial positions, the class of surplus-invariant acceptance sets. These are characterized by the fact that acceptability …

Order book dynamics play an important role in both execution time and price formation of orders in an exchange market. In this study, we aim to model the limit order arrival rates in the vicinity of the best bid and the best ask price levels. We use limit order book data for Garanti Bank, which is one of the most trade…

Under Markovian assumptions, we leverage a Central Limit Theorem (CLT) for the empirical measure in the test statistic of the composite hypothesis Hoeffding test so as to establish weak convergence results for the test statistic, and, thereby, derive a new estimator for the threshold needed by the test. We first show t…

Optimal distributed testing under communication constraints with shared randomness.

Study reveals limits of detecting local geometry in random graphs.

Proposes a modified Morgan-Pitman test for evaluating variances in machine learning models.

Randomization tests rely on simple data transformations and possess an appealing robustness property. In addition to being finite-sample valid if the data distribution is invariant under the transformation, these tests can be asymptotically valid under a suitable studentization of the test statistic, even if the invari…

New findings control FDR for online testing methods under positive dependence.

This paper surveys some recent developments in fundamental limits and optimal algorithms for network analysis. We focus on minimax optimal rates in three fundamental problems of network analysis: graphon estimation, community detection, and hypothesis testing. For each problem, we review state-of-the-art results in the…

A fundamental problem in network data analysis is to test Erdös-Rényi model $\mathcal{G}\left(n,\frac{a+b}{2n}\right)$ versus a bisection stochastic block model $\mathcal{G}\left(n,\frac{a}{n},\frac{b}{n}\right)$, where $a,b>0$ are constants that represent the expected degrees of the graphs and $n$ denotes the number o…

Study controls error rates of binary classifiers using hypothesis testing.