In this article, we address the statistical inference problem proposed for the sparse spatio-temporal autoregressive models with additive measurement error when the number of spatial nodes exceeds the number of temporal observations. We use the improved Yule-Walker estimation method, adding the bagging algorithm to the estimation process to solve the over-identification problem. The simulation-extrapolation (SIMEX) method is used to reduce the influence of additive measurement error and we confirm the feasibility of empirical likelihood method to establish confidence intervals for model coefficients. Furthermore, some simulations and real examples are carried out to evaluate the finite sample performance.
When estimating the variance from a sample, usually the so-called Bessel's correction is used, that is, unintuitively each term is weighted by the sample size n minus one. Although this is an unbiased estimator, it does not necessarily yield the best accuracy in terms of bias-variance tradeoff. To this end, we conducted bibliometric work and observe that many statistics textbooks recommend Bessel's correction for somewhat spurious reasons. Furthermore, we address the bias-variance tradeoff in variance estimation from a theoretical perspective and show that usually the uncorrected version of the sample variance is a better choice. We back this up with a simulation study that can be conducted in a classroom setting, where students can learn about unbiasedness, bias-variance tradeoff, conducting simulation studies, and estimation in general from an easy example.
This article presents methods for estimating extreme probabilities, beyond the range of the observations. These methods are model-free and applicable to almost any sample size. They are grounded in order statistics theory and have a wide range of applications, as they simply require the assumption of a finite expectation. Even in cases when a particular risk model exists, the new methods provide clarity, security and simplicity. The methodology is applicable to the behavior of financial markets, and the results are comparable to those provided by extreme value theory.
This study addresses the often-overlooked issue of measurability at intermediate points when applying Taylor's theorems to random functions and random vectors (e.g., likelihood functions with respect to estimators) in statistics. Classical Taylor-related theorems were originally developed for deterministic settings. Consequently, they do not directly extend to stochastic functions and variables and do not inherently guarantee the measurability of intermediate points. In statistical contexts, applying these theorems without properly accounting for randomness can lead to analyses that lack well-defined probabilistic interpretations. Elementary approaches, such as pointwise constructions, are insufficient for handling random quantities and establishing measurable intermediate points. Moreover, some statistical literature has implicitly disregarded this issue, often neglecting the stochastic nature of the problem and assuming that intermediate points are measurable. To address this gap, we develop multivariate Taylor's and mean value theorems tailored for random functions and random variables under mild assumptions. We provide illustrative examples demonstrating the applicability of our results to commonly used statistical methods, including maximum likelihood estimation, M-estimation, and profile estimation. Our findings contribute a rigorous foundation for the applications of Taylor expansions in statistics.
Financial institutions are required to hold capital reserves to protect against future losses, and many rely on mathematical models to estimate the necessary amounts. While these models can make risk measurement more precise, they are often used by practitioners who may not fully grasp their assumptions or limitations. One recurring source of error lies in the treatment of correlation-the statistical link between different risks-which plays a crucial role in determining how losses might combine. Misjudging these relationships has, in the past, amplified systemic vulnerabilities, most famously in the misuse of the Gaussian copula model during the subprime crisis. This article revisits the problem of correlation mistaken beliefs from a pedagogical standpoint, using simplified examples and reproducible R code to show how small misunderstandings can have large consequences. The discussion aims to encourage greater critical awareness of quantitative tools among risk managers, regulators, and students alike.
Inspired by recommendations commonly encountered in introductory statistics classes to perform model checking and make modeling decisions based on visual inspections of diagnostic plots, we implemented and administered a survey on interpretation of a variety of diagnostic plots across multiple settings. We summarize the patterns in the answers provided by more than 300 undergraduate and graduate students enrolled in statistic courses via a mixed effects model exploring the impact of different data-generating settings and various plot features. Notably, we find that the students surveyed here are comparable to random chance at making the correct decisions on the basis of the plots they were shown. The implications of this uncertainty and the lack of reproducibility introduced by the model checking/model selection process are explored in depth in one of the settings presented to demonstrate the consequences of using subjective and frequently sub-optimal human judgments to make modeling choices.
Laboratories use group testing to test high volumes of clinical specimens for pathogens, such as SARS-CoV-2, West Nile, and Chlamydia trachomatis. The process works by testing multiple specimens together as an amalgamation, rather than testing each specimen separately, to reduce the number of tests needed. There are many different algorithmic ways to apply group testing. The role of a statistician is to recommend an algorithm that will perform "best" relative to the information available, such as disease prevalence. Algorithms are most often compared by their expected number of tests needed for an application, where a lower value is preferred. Unfortunately, this measure alone does not account for some algorithms having a lower expected number of tests at the expense of being much more complex to implement. For this reason, we propose a new measure that we refer to as the complexity. In our article, we present its definition and derive its expression for several common algorithms. We show that some algorithms may be too complex for implementation, while others should become more widely used. Our proposed measure is illustrated with a SARS-CoV-2 testing implementation. R functions and a Shiny app are provided to perform calculations.
Circular statistics deals with the analysis of circular data, which are data collected on a circle. Such data is periodic in nature and is commonly collected in many fields. An important question often asked when analyzing circular data is whether or not the data are sampled from a uniform distribution. In this article, we explain how Beran's commonly used tests of uniformity work, and building on this work, we show how to construct new tests. Lastly, we show how seemingly unrelated alternative distributions are related through such tests.
Bayesian Model Averaging (BMA) enhances predictive performance by integrating over competing models, but its scalability is often limited by the computational burden of Markov chain Monte Carlo (MCMC)-based posterior inference. Recent variational approaches such as VBMA (Kejzlar et al.) offer scalability but rely on restrictive mean-field assumptions that fail to capture posterior dependencies, leading to suboptimal uncertainty quantification in complex settings. We propose Neural Autoregressive Flow Bayesian Model Averaging (NAF-BMA), a novel variational BMA framework that replaces the simple variational family with expressive neural autoregressive flows. This innovation enables NAF-BMA to model highly correlated, multimodal posterior structures with MCMC-level accuracy while retaining near-VBMA scalability. The method jointly estimates individual model evidences and posterior model probabilities within a unified optimization scheme, producing an optimal combined posterior over the entire model space. Designed as a general and modular framework requiring minimal model-specific derivations, NAF-BMA extends naturally to a broad class of Bayesian models. Across extensive simulation and real-data studies, it consistently outperforms VBMA and closely matches MCMC accuracy, establishing NAF-BMA as a flexible and scalable new paradigm for Bayesian model averaging.
The increasing availability of secondary data creates new opportunities for statisticians, but it can lead to distance between statisticians and the communities impacted by the results of their analysis. This distance can decrease the effectiveness of research based on secondary datasets and indicate potential ethical concerns. To respond to this concern, we discuss how principles of Community-Based Participatory Research (CBPR) can be adapted to the setting of conducting quantitative research with secondary data. To provide actionable guidance for researchers entering this field, we examine three key areas of existing work in detail: foundational literature on CBPR, quantitative research conducted within community contexts, and scholarship on statistics community service-learning courses. We then emphasize synergies between CBPR and secondary data analysis that are present throughout the research process. We discuss specific examples of partnerships between statisticians and community groups and/or members that use secondary data analysis to illustrate how statisticians can successfully carry out these collaborations.
Statistical methods depend on the satisfaction of assumptions about the data generating process in order for theoretical and demonstrated properties to hold. It is also implicitly assumed that methods are used as intended. This work presents evidence that, without strong scaffolding, the implicit assumption around proper implementation is frequently not satisfied and that substantial implementation gaps exist between methods' theoretical properties and performance in applied contexts. We introduce thinkCausal, a novel causal inference tool, as an example of how scaffolded statistical software can increase the usability of statistical methods and reduce existing implementation gaps. We draw evidence from a randomized study where participants were asked to estimate a causal effect within one of three treatment arms: (a) using thinkCausal, a scaffolded point and click implementation of Bayesian Additive Regression Trees (BART) for causal inference, (b) using bartCause, an R package implementation of Bayesian Additive Regression Trees (BART) for causal inference, or (c) using a software and method of their own choosing. Results show that participants were only able to reliably obtain accurate results when using thinkCausal.
