arXiv subjects

Kenichi Hayashi

Publications and source records attributed to Kenichi Hayashi.

7 recordsLinked to original sources

arXiv2026

A Direct Variance Estimation (DiVE) for Meta-Analysis of Median Differences

Meta-analyses of two-group studies that report median differences typically rely on methods that require, in addition to the median difference and sample size, summary measures of dispersion such as quartiles or ranges. Studies that do not report such statistics are often excluded from the meta-analysis. Existing two-stage approaches first estimate the asymptotic variance of the median difference within each study under parametric assumptions, and then combine these study-specific estimates to obtain the pooled median difference and its variance. We propose Direct Variance Estimation (DiVE), a method that directly estimates the variance of the pooled difference using only study-level median differences and their sample sizes. A comprehensive simulation study across a wide range of distributional scenarios shows that DiVE performs comparably to or better than conventional two-stage methods, with clear advantages when the number of studies is small. A re-analysis of published meta-analyses demonstrates that DiVE enables the inclusion of studies lacking dispersion statistics, leading to a more comprehensive and potentially less biased synthesis of evidence.

stat.ME↗

arXiv2025

Statistical Inference of the Matthews Correlation Coefficient for Multiclass Classification

Classification problems are essential statistical tasks that form the foundation of decision-making across various fields, including patient prognosis and treatment strategies for critical conditions. Consequently, evaluating the performance of classification models is of significant importance, and numerous evaluation metrics have been proposed. Among these, the Matthews correlation coefficient (MCC), also known as the phi coefficient, is widely recognized as a reliable metric that provides balanced measurements even in the presence of class imbalance. However, with the increasing prevalence of multiclass classification problems involving three or more classes, macro-averaged and micro-averaged extensions of MCC have been employed, despite a lack of clear definitions or established references for these extensions. In the present study, we propose a formal framework for MCC tailored to multiclass classification problems using macro-averaged and micro-averaged approaches. Moreover, discussions on the use of these extended MCCs for multiclass problems often rely solely on point estimates, potentially overlooking the statistical significance and reliability of the results. To address this gap, we introduce several methods for constructing asymptotic confidence intervals for the proposed metrics. Furthermore, we extend these methods to include the construction of asymptotic confidence intervals for differences in the proposed metrics, specifically for paired study designs. The utility of our methods is evaluated through comprehensive simulations and real-world data analyses.

stat.ME↗

arXiv2025

On a class of binary regression models and their robust estimation

A robust estimation framework for binary regression models is studied, aiming to extend traditional approaches like logistic regression models. While previous studies largely focused on logistic models, we explore a broader class of models defined by general link functions. We incorporate various loss functions to improve estimation under model misspecification. Our investigation addresses robustness against outliers and model misspecifications, leveraging divergence-based techniques such as the $β$-divergence and $γ$-divergence, which generalize the maximum likelihood approach. These divergences introduce loss functions that mitigate the influence of atypical data points while retaining Fisher consistency. We establish a theoretical property of the estimators under both correctly specified and misspecified models, analyzing their robustness through quantifying the effect of outliers in linear predictor. Furthermore, we uncover novel relationships between existing estimators and robust loss functions, identifying previously unexplored classes of robust estimators. Numerical experiments illustrate the efficacy of the proposed methods across various contamination scenarios, demonstrating their potential to enhance reliability in binary classification tasks. By providing a unified framework, this study highlights the versatility and robustness of divergence-based methods, offering insights into their practical application and theoretical underpinnings.

stat.ME↗

arXiv2025

Robust Estimation of Item Parameters via Divergence Measures in Item Response Theory

Marginal maximum likelihood estimation (MMLE) in item response theory (IRT) is highly sensitive to aberrant responses, such as careless answering and random guessing, which can reduce estimation accuracy. To address this issue, this study introduces robust estimation methods for item parameters in IRT. Instead of empirically minimizing Kullback--Leibler divergence as in MMLE, the proposed approach minimizes the objective functions based on robust divergences, specifically density power divergence and γ-divergence. The resulting estimators are statistically consistent and asymptotically normal under appropriate regularity conditions. Furthermore, they offer a flexible trade-off between robustness and efficiency through hyperparameter tuning, forming a generalized estimation framework encompassing MMLE as a special case. To evaluate the effectiveness of the proposed methods, we conducted simulation experiments under various conditions, including scenarios with aberrant responses. The results demonstrated that the proposed methods surpassed existing ones in performance across various conditions. Moreover, numerical analysis of influence functions verified that increasing the hyperparameters effectively suppressed the impact of responses with low occurrence probabilities, which are potentially aberrant. These findings highlight that the proposed approach offers a robust alternative to MMLE, significantly enhancing measurement accuracy in testing and survey contexts prone to aberrant responses.

stat.ME↗

arXiv2024

Asymptotic Properties of Matthews Correlation Coefficient

Evaluating classifications is crucial in statistics and machine learning, as it influences decision-making across various fields, such as patient prognosis and therapy in critical conditions. The Matthews correlation coefficient (MCC) is recognized as a performance metric with high reliability, offering a balanced measurement even in the presence of class imbalances. Despite its importance, there remains a notable lack of comprehensive research on the statistical inference of MCC. This deficiency often leads to studies merely validating and comparing MCC point estimates, a practice that, while common, overlooks the statistical significance and reliability of results. Addressing this research gap, our paper introduces and evaluates several methods to construct asymptotic confidence intervals for the single MCC and the differences between MCCs in paired designs. Through simulations across various scenarios, we evaluate the finite-sample behavior of these methods and compare their performances. Furthermore, through real data analysis, we illustrate the potential utility of our findings in comparing binary classifiers, highlighting the possible contributions of our research in this field.

stat.ME↗

arXiv2014

Model-based clustering of multivariate binary data with dimension reduction

Clustering methods with dimension reduction have been receiving considerable wide interest in statistics lately and a lot of methods to simultaneously perform clustering and dimension reduction have been proposed. This work presents a novel procedure for simultaneously determining the optimal cluster structure for multivariate binary data and the subspace to represent that cluster structure. The method is based on a finite mixture model of multivariate Bernoulli distributions, and each component is assumed to have a low-dimensional representation of the cluster structure. This method can be considered an extension of the traditional latent class analysis model. Sparsity is introduced to the loading values, which produces the low-dimensional subspace, for enhanced interpretability and more stable extraction of the subspace. An EM-based algorithm is developed to efficiently solve the proposed optimization problem. We demonstrate the effectiveness of the proposed method by applying it to a simulation study and real datasets.

stat.ME↗

arXiv2010

Gigantic Maximum of Nanoscale Noncontact Friction

We report measurements of noncontact friction between surfaces of NbSe$_{2}$ and SrTiO$_{3}$, and a sharp Pt-Ir tip that is oscillated laterally by a quartz tuning fork cantilever. At 4.2 K, the friction coefficients on both the metallic and insulating materials show a giant maximum at the tip-surface distance of several nanometers. The maximum is strongly correlated with an increase in the spring constant of the cantilever. These features can be understood phenomenologically by a distance-dependent relaxation mechanism with distributed time scales.

cond-mat.mtrl-sci↗