arXiv subjects

Ori Davidov

Publications and source records attributed to Ori Davidov.

7 recordsLinked to original sources

arXiv2026

Testing for lack of fit in paired comparison data

Linear stochastic transitivity is a central assumption in paired comparison models that is rarely verified in practice. Empirical violations, however, are common and can substantially affect inference and ranking. We develop a class of tests for detecting lack of fit in cardinal paired comparison models, where lack of fit is characterized by the presence of cyclical preferences among subsets of items. We propose a suite of tests adapted to different regimes governing the growth of the comparison graph. For a fixed number of items, the proposed procedures exhibit substantially improved power relative to the classical Kendall--Smith test and its cardinal analogue. We further extend the framework to high--dimensional, sparse comparison graphs near the connectivity threshold in random graph models. The theoretical analysis characterizes the behavior of the tests under both the null and alternative, with particular emphasis on limits of detectability and consistency. Simulation studies corroborate the theoretical findings, and applications to real data uncover substantial and previously unrecognized intransitivity and structural lack of fit.

stat.ME↗

arXiv2026

Safe hypotheses testing with application to order restricted inference

Hypothesis tests under order restrictions arise in a wide range of scientific applications. By exploiting inequality constraints, such tests can achieve substantial gains in power and interpretability. However, these gains come at a cost: when the imposed constraints are misspecified, the resulting inferences may be misleading or even invalid, and Type III errors may occur, i.e., the null hypothesis may be rejected when neither the null nor the alternative is true. To address this problem, this paper introduces safe tests. Heuristically, a safe test is a testing procedure that is asymptotically free of Type III errors. The proposed test is accompanied by a certificate of validity, a pre--test that assesses whether the original hypotheses are consistent with the data, thereby ensuring that the null hypothesis is rejected only when warranted, enabling principled inference without risk of systematic error. Although the development in this paper focus on testing problems in order--restricted inference, the underlying ideas are more broadly applicable. The proposed methodology is evaluated through simulation studies and the analysis of well--known illustrative data examples, demonstrating strong protection against Type III errors while maintaining power comparable to standard procedures.

stat.ME↗

arXiv2024

Modeling cyclicality and intransitivity in paired comparisons data

Paired comparison data arise in ranking problems, decision analysis, sports analytics, recommendation systems, and many other applications in which alternatives are evaluated by comparing two items at a time. Standard models typically impose a transitive preference profile induced by a vector of merits. In many empirical settings, however, preference relations exhibit cyclic and intransitive patterns that cannot be adequately represented by a global ranking. This paper develops a framework for modeling cyclicality and departures from transitivity. The proposed approach decomposes a preference profile into orthogonal transitive and cyclic components and provides a geometric characterization of the associated parameter space. The cyclic component is represented using an overcomplete dictionary of elementary cycles, so that identifying cyclic structure and the intransitivities it may induce becomes a sparse model selection problem. We propose a method for recovering sparse cyclic structure and establish large--sample guarantees for estimation and model recovery. The analysis clarifies the relationship between cyclicality, intransitivity, and several notions of transitivity used in paired comparison theory. By explicitly modeling cyclic structure, the proposed framework can improve estimation, ranking, interpretation, and prediction. The methodology is evaluated through simulations and illustrated with an empirical application.

stat.ME↗

arXiv2024

Least squares for cardinal paired comparisons data

Least square estimators for graphical models for cardinal paired comparison data with and without covariates are rigorously analyzed. Novel, graph--based, necessary and sufficient conditions that guarantee strong consistency, asymptotic normality and the exponential convergence of the estimated ranks are emphasized. A complete theory for models with covariates is laid out. In particular, conditions under which covariates can be safely omitted from the model are provided. The methodology is employed in the analysis of both finite and infinite sets of ranked items where the case of large sparse comparison graphs is addressed. The proposed methods are explored by simulation and applied to the ranking of teams in the National Basketball Association (NBA).

stat.ME↗

arXiv2020

On the use of historical estimates

The use of historical estimates in current studies is common in a wide variety of application areas. Nevertheless, despite their routine use the uncertainty associated with historical estimates is rarely properly accounted for in the analysis. In this communication we review common practices and then provide a mathematical formulation and a principled methodology for addressing the problem of drawing inferences in the presence of historical data. Three distinct variants are investigated in detail; the corresponding limiting distributions are found and compared. The design of future studies, given historical data, is also explored and relations with a variety of other well--studied statistical problems discussed.

stat.ME↗

arXiv2016

Analysis of High Dimensional Compositional Data Containing Structural Zeros with Applications to Microbiome Data

This paper is motivated by the recent interest in the analysis of high dimen- sional microbiome data. A key feature of this data is the presence of `structural zeros' which are microbes missing from an observation vector due to an underlying biological process and not due to error in measurement. Typical notions of missingness are insufficient to model these structural zeros. We define a general framework which allows for structural zeros in the model and propose methods of estimating sparse high dimensional covariance and precision matrices under this setup. We establish error bounds in the spectral and frobenius norms for the proposed esti- mators and empirically support them with a simulation study. We also apply the proposed methodology to the global human gut microbiome data of Yatsunenko (2012).

stat.AP↗

arXiv2013

The linear stochastic order and directed inference for multivariate ordered distributions

Researchers are often interested in drawing inferences regarding the order between two experimental groups on the basis of multivariate response data. Since standard multivariate methods are designed for two-sided alternatives, they may not be ideal for testing for order between two groups. In this article we introduce the notion of the linear stochastic order and investigate its properties. Statistical theory and methodology are developed to both estimate the direction which best separates two arbitrary ordered distributions and to test for order between the two groups. The new methodology generalizes Roy's classical largest root test to the nonparametric setting and is applicable to random vectors with discrete and/or continuous components. The proposed methodology is illustrated using data obtained from a 90-day pre-chronic rodent cancer bioassay study conducted by the National Toxicology Program (NTP).

math.ST↗