arXiv subjects

Herman Tesso

Publications and source records attributed to Herman Tesso.

2 recordsLinked to original sources

arXiv2026

High-Dimensional Data with Measurement Error

In many important statistical analyses, the number of covariates $p$ often exceeds the data size $n$, a regime commonly referred to as high-dimensional. While considerable progress has been made in high-dimensional regression under the assumption of error-free covariates, real-world data frequently involve noisy or corrupted measurements. When left unaddressed, measurement errors can silently distort the analysis and mislead the conclusions. This paper reviews and evaluates some advisable statistical inference methods for high-dimensional regression in the presence of mismeasured covariates. We discuss four penalized regression methods -- ridge, lasso, Dantzig selector, and Elastic-net -- alongside their measurement-error-corrected variants, and conduct a comparative study under linear additive and uncorrelated measurement error models. Through simulation studies and a real application to high-dimensional medical genetic data, we illustrate the methods studied, show that the choice of correction procedure is problem-specific, and provide practical recommendations to help practitioners navigate this methodological landscape.

stat.ME↗

arXiv2026

LOO-PIT predictive model checking

We consider predictive checking for Bayesian model assessment using leave-one-out probability integral transform (LOO-PIT). LOO-PIT values are conditional cumulative predictive probabilities given LOO predictive distributions and corresponding left out observations. For a well-calibrated model, LOO-PIT values should be near uniformly distributed, but in the finite sample case they are not independent, due to LOO predictive distributions being determined by nearly the same data (all but one observation). We prove that this dependency is non-negligible in the finite case and depends on model complexity. We propose three testing procedures that can be used for continuous and discrete dependent uniform values. We also propose an automated graphical method for visualizing local departures from the null. Extensive numerical experiments on simulated and real datasets demonstrate that the proposed tests achieve competitive performance overall and have much higher power than standard uniformity tests based on the independence assumption that inevitably lead to lower than expected rejection rate.

stat.ME↗