Department of Data Science and Analytics

Mathematics and Computers in Simulation 250 p. 152-177 Doi: https://doi.org/10.1016/j.matcom.2026.06.024

Applied Numerical Mathematics 227 p. 204-231 Doi: https://doi.org/10.48550/arXiv.2511.01587

Psychometrika p. 32-32 Doi: https://doi.org/10.1017/psy.2026.10135

Mean and sum scores are widely used in psychometric practice, but their behavior under weak assumptions is not fully understood. We study two basic questions under a latent variable framework with increasing-item asymptotics: when does the observed mean score approximate the true score of the administered form, and when is a true score insensitive to removing a vanishing fraction of items? For the first question, we introduce martingale factor models, which, for polytomous items, weaken conditional independence to a conditional-mean restriction, yet still yield concentration and asymptotic normality results for mean scores around their true scores. For the second question, we show that this stability is equivalent to the convergence of the true scores when the items are bounded, and we identify conditions under which this convergence takes place. These results clarify when mean scores can be interpreted as stable proxies for latent variables, and yield psychometrically relevant consequences. Several theoretical and numerical illustrations are given, including a new interpretation of large-form mean-score correlations and a person-specific confidence interval procedure for the true score.

Structural Equation Modeling p. 5-5 Doi: https://doi.org/10.1080/10705511.2026.2651100

Muda and Yangxuan recommended a ridge-calibrated test statistic for controlling Type I error inflationin confirmatory factor analysis under non-normality. Although improving finite-sample inference is animportant goal, their empirical evaluation is undermined by incorrectly implemented benchmark statis-tics, misattributed comparison methods, and a simulation design restricted to asymptotically robustconditions. Using corrected code, we reanalyze the original conditions and replace the misattributedbenchmarks with the penalized eigenvalue procedures pEBA4RLS and pOLS2RLS: Under the originalconditions, the best-performing procedures are the ridge-calibrated TCsFCr statistic and the penalizedeigenvalue methods. However, under additional non-asymptotically robust conditions, including high-dimensional models, pEBA4RLS provides the most reliable Type I error control and outperforms theridge-calibrated competitors.

Applied Mathematical Finance Doi: https://doi.org/10.1080/1350486X.2026.2659017

We present a novel perspective on the universal approximation theorem for rough path functionals, introducing a polynomial-based approximation class. We extend universal approximation to non-geometric rough paths within the tensor algebra. This development addresses critical needs in finance, where no-arbitrage conditions necessitate Itô integration. Furthermore, our findings motivate a hypothesis for payoff functionals in financial markets, allowing straightforward analysis of signature payoffs proposed in Arribas (Derivatives Pricing Using Signature Payoffs; 2018).