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arXiv research

A locally-built, LLM-digested index of recent arXiv papers in quant finance, geometry/topology, and statistical ML — keyword search served straight from SQLite on this machine.

168,657 papers · 148 categories

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59118176235 · Jun 202019922001200920172026
48 results for chi-square statistic

The paper develops approximations for Pearson's chi-square statistic and applies them to confidence intervals.

problem Finding confidence intervals for strictly convex functions of discrete distribution weights.
method Non-asymptotic local normal approximation for multinomial probabilities, deriving bounds and coupling inequalities.
result Developed methods to find confidence intervals for negative entropy of discrete distributions.

USP test improves on Pearson's chi-squared and GG-test for independence.

problem Deficiencies in Pearson's chi-squared and GG-test for independence.
method USP test based on UU-statistic estimator of population dependence measure.
result USP test controls size, handles small cell counts, and detects minimal violations of independence.

Develops an empirical likelihood framework for random forests and ensembles.

problem Quantifying the statistical uncertainty of random forests and ensembles.
method Empirical likelihood framework exploiting the incomplete UU-statistic structure of ensemble predictions.
result Modified empirical likelihood statistic achieves accurate coverage and practical reliability.

Distance correlation has gained much recent attention in the data science community: the sample statistic is straightforward to compute and asymptotically equals zero if and only if independence, making it an ideal choice to discover any type of dependency structure given sufficient sample size. One major bottleneck is…

2019-12-27abs ↗pdf ↗

New SQ lower bounds for NGCA without requiring chi-squared condition.

problem Proving SQ hardness for NGCA under moment-matching conditions.
method General SQ lower bound methodology applied to NGCA under moment-matching conditions.
result Proved near-optimal SQ lower bounds for NGCA without chi-squared condition.

We study the information content of nuclear masses from the perspective of global models of nuclear binding energies. To this end, we employ a number of statistical methods and diagnostic tools, including Bayesian calibration, Bayesian model averaging, chi-square correlation analysis, principal component analysis, and …

2020-02-11abs ↗pdf ↗

This paper provides performance guarantees for neural estimation of statistical distances.

problem Developing performance guarantees for neural estimation of statistical distances.
method Non-asymptotic error bounds using function approximation theorems and empirical process theory.
result Established a fundamental tradeoff between approximation and estimation errors in neural estimation of statistical distances.

The transition probability of a Cox-Ingersoll-Ross process can be represented by a non-central chi-square density. First we prove a new representation for the central chi-square density based on sums of powers of generalized Gaussian random variables. Second we prove Marsaglia's polar method extends to this distributio…

2008-02-29abs ↗pdf ↗

A goodness-of-fit test for DCSBM improves scalability and power for large sparse networks.

problem Testing goodness-of-fit for degree-corrected stochastic block models (DCSBM) in large sparse networks.
method Proposes an adjusted chi-square test statistic for multinomial distributions, adjusted for degree-corrected networks, and applies it to compressed adjacency matrices.
result The test statistic converges in distribution under null, and is consistent in recovering the number of communities.

PQMass assesses generative model quality using chi-squared tests.

problem Assessing the quality of generative models without density assumptions.
method Divides sample space into regions, applies chi-squared tests to p-values.
result Effectively assesses generative model quality, novelty, and diversity.

Four new methods for computing generalized chi-square distribution.

problem Computing the generalized chi-square distribution accurately and efficiently.
method Two exact and two approximate methods, with software for cdf, pdf, and inverse cdf.
result Comparison of methods' accuracy and speed, identifying best for different cases.

Study tests uniformity of categorical data against missing-ball alternatives, finding chi-squared test outperforms.

problem Testing uniformity of categorical data against missing-ball alternatives.
method Characterizes minimax risk, uses collisions and chi-squared test, reduces to structured subset of alternatives.
result Minimax test outperforms chi-squared test under least favorable alternative.

Study compares statistical properties and power of divergence measures for credit risk monitoring.

problem Detecting distributional shifts in credit risk models.
method Derives statistical properties and chi-square benchmark values for Jensen-Shannon Divergence and Kullback-Leibler Divergence, demonstrating their applicability in credit risk monitoring.
result Jensen-Shannon Divergence and Kullback-Leibler Divergence follow chi-square distributions and reveal practical trade-offs in minimizing false positives vs. detecting changes.

Network data is prevalent in many contemporary big data applications in which a common interest is to unveil important latent links between different pairs of nodes. Yet a simple fundamental question of how to precisely quantify the statistical uncertainty associated with the identification of latent links still remain…

2019-10-03abs ↗pdf ↗

SBI provides more accurate pole positions than chi-squared minimization in model misspecification.

problem Accurate pole position estimation in pi-pi scattering models.
method Simulation Based Inference (SBI) method compared to chi-squared minimization.
result SBI leads to more robust predictions of pole positions in models of pi-pi scattering.

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 …

2019-02-16abs ↗pdf ↗

EL framework certifies and flags bias in ML models without distributional assumptions.

problem Systematic performance disparities across sensitive subpopulations in ML models.
method Empirical likelihood-based approach for non-parametric fairness auditing.
result EL framework outperforms bootstrap methods in certification and subpopulation discovery.

LMC algorithm converges to target in Chi-squared and Renyi divergence.

problem Sampling from target distribution using LMC with strong dissipativity and smoothness conditions.
method LMC algorithm with strong dissipativity and first-order smoothness, initialized with Gaussian.
result LMC reaches ε-neighborhood of target in Chi-squared and Renyi divergence in O(λ²dε⁻¹) steps.

Study compares chi-squared divergence and KL-divergence posteriors for PAC-Bayesian bounds.

problem Investigates optimal posteriors for PAC-Bayesian bounds using chi-squared divergence.
method Analyzes bounds for three distance functions, derives FP equations for computation.
result Chi-squared divergence based posteriors have weaker bounds and worse test errors.

We consider the problem of comparing probability densities between two groups. A new probabilistic tensor product smoothing spline framework is developed to model the joint density of two variables. Under such a framework, the probability density comparison is equivalent to testing the presence/absence of interactions.…

2019-11-06abs ↗pdf ↗

Efficient ANN search for sparse embeddings in ads targeting.

problem Efficiently searching near neighbors in sparse data for applications like ads targeting.
method Graph-based ANN algorithms (HNSW, chi-square two-tower model, Sign Cauchy Projections).
result Sparse embeddings and ANN algorithms improve efficiency in EBR applications.

This paper tests the multivariate normality of node degrees in Erdős-Rényi graphs.

problem Testing the multivariate normality of node degrees in Erdős-Rényi graphs.
method Chi-square goodness of fit test, Anderson-Darling test, CDF comparison, maximum likelihood estimation.
result The degrees of nodes in Erdős-Rényi graphs do not follow a multivariate normal distribution, but the approximation is valid for large values of n and p.

RENAL test evaluates generative models for time series data.

problem Evaluating generative models for time series data is challenging.
method RENAL test uses recurrent neural networks to transform time series into conditionally independent data pairs for goodness-of-fit testing.
result RENAL test outperforms existing methods in evaluating generative models for time series data.

Group Shapley evaluates feature groups in business data, improving explainability in AI.

problem Evaluating the importance of feature groups in business and economic data.
method Developed Group Shapley and a significance testing procedure based on chi-square approximation.
result Market-related variables are identified as the most influential feature group.

A theory which describes the share price evolution at financial markets as a continuous-time random walk has been generalized in order to take into account the dependence of waiting times t on price returns x. A joint probability density function (pdf) which uses the concept of a Lévy stable distribution is worked out.…

2003-10-15abs ↗pdf ↗

A test for neural networks identifies genetic associations.

problem Testing complex associations in neural networks.
method Sieve quasi-likelihood ratio test for neural networks with one hidden layer.
result The test statistic has an asymptotic chi-squared distribution.

Neural networks estimate statistical divergences with performance guarantees.

problem Estimating statistical divergences with theoretical performance guarantees.
method Parametrizing empirical variational form by a neural network and optimizing over parameter space.
result Established non-asymptotic absolute error bounds for neural estimators of four f\mathsf{f}-divergences.

Test partial effects in Frechet regression on Bures-Wasserstein manifolds.

problem Assessing partial effects in Frechet regression on complex manifolds.
method Sample splitting strategy to estimate covariance matrices and test statistic convergence.
result The test statistic converges to a weighted mixture of chi squared components.

Kernel two-sample testing is a useful statistical tool in determining whether data samples arise from different distributions without imposing any parametric assumptions on those distributions. However, raw data samples can expose sensitive information about individuals who participate in scientific studies, which make…

2018-08-01abs ↗pdf ↗

Zigzag sampling algorithm efficiently samples from strongly log-concave distributions with low computational cost.

problem Sampling from strongly log-concave distributions efficiently and with low computational complexity.
method Zigzag sampling algorithm with warm start assumption, focusing on gradient evaluations.
result Achieves ε error in chi-square divergence with computational cost of O(κ²d^(1/2)(log(1/ε))^(3/2)) gradient evaluations.

Transformers learn to adapt to different task difficulties and resist distribution shifts.

problem Understanding and optimizing a Transformer's performance across various task difficulties and distribution shifts.
method Analyzing a pretrained Transformer on a mixture distribution of tasks, proving optimal convergence rates.
result Transformers achieve optimal convergence rates on tasks of specific difficulty levels, robust to distribution shifts.

ff-divergences are a general class of divergences between probability measures which include as special cases many commonly used divergences in probability, mathematical statistics and information theory such as Kullback-Leibler divergence, chi-squared divergence, squared Hellinger distance, total variation distance e…

2013-02-02abs ↗pdf ↗

AES scheme improves Bermudan and American option pricing for Heston models.

problem Pricing Bermudan and American options under Heston models efficiently.
method AES scheme using non-central chi-square distribution for variance process.
result AES achieves higher accuracy and computational efficiency for Bermudan options.

Improved Bayesian analysis for SVM models using a mixture sampler.

problem Efficient simulation-based analysis of stochastic volatility in mean models.
method Developed a generalized mixture sampler for SVM models, approximating non-central chi-squared distributions as mixtures of normal distributions.
result The proposed method outperforms other volatility models based on marginal likelihoods in empirical studies.

Study robust hypothesis testing under Hellinger distance, proving lower bounds and providing tests.

problem Testing close variants of specified distributions robustly to Hellinger distance.
method Lower bound on slack factor, testing with Hellinger balls, symmetric chi-squared distance analysis.
result Lower bound on slack factor quantifies robustness under misspecification.