In observational causal inference studies, unmeasured confounding remains a critical threat to the validity of effect estimates. While proximal causal inference (PCI) has emerged as a powerful framework for mitigating such bias through proxy variables, existing PCI methods cannot directly handle censored data. This article develops a unified proximal causal inference framework that simultaneously addresses unmeasured confounding and right-censoring challenges, extending the proximal causal inference literature. Our key contributions are twofold: (i) We propose novel identification strategies and develop two distinct estimators for the censored-outcome bridge function and treatment confounding bridge function, resolving the fundamental challenge of unobserved outcomes; (ii) To improve robustness against model misspecification, we construct a robust proximal estimator and establish uniform consistency for all proposed estimators under mild regularity conditions. Through comprehensive simulations, we demonstrate the finite-sample performance of our methods, followed by an empirical application evaluating right heart catheterization effectiveness in critically ill ICU patients.

We propose a new unit distribution, study its properties, and provide an important application in the field of geology through a set of risk indicators. We test its practicality through two applications to real data, make comparisons with the well-known beta and Kumaraswamy distributions, and estimate the parameters of the new distribution in different ways. We provide a new regression model and apply it in statistical prediction operations for residence times data.

Testing interval hypotheses is of huge relevance in the biomedical and cognitive sciences; for example, in clinical trials. Frequentist approaches include the proposal of equivalence tests, which have been used to study if there is a predetermined meaningful treatment effect. In the Bayesian paradigm, two popular approaches exist: The first is the region of practical equivalence (ROPE), which has become increasingly popular in the cognitive sciences. The second is the Bayes factor for interval null hypotheses, which was proposed by Morey et al. One advantage of the ROPE procedure is that, in contrast to the Bayes factor, it is quite robust to the prior specification. However, while the ROPE is conceptually appealing, it lacks a clear decision-theoretic foundation like the Bayes factor. In this paper, a decision-theoretic justification for the ROPE procedure is derived for the first time, which shows that the Bayes risk of a decision rule based on the highest-posterior density interval (HPD) and the ROPE is asymptotically minimized for increasing sample size. To show this, a specific loss function is introduced. This result provides an important decision-theoretic justification for testing the interval hypothesis in the Bayesian approach based on the ROPE and HPD, in particular, when sample size is large.

The current replication crisis relating to the non-replicability and the untrustworthiness of published empirical evidence is often viewed through the lens of the Positive Predictive Value (PPV) in the context of the Medical Diagnostic Screening (MDS) model. The PPV is misconstrued as a measure that evaluates `the probability of rejecting H0 when false’, after being metamorphosed by replacing its false positive/negative probabilities with the type I/II error probabilities. This perspective gave rise to a widely accepted diagnosis that the untrustworthiness of published empirical evidence stems primarily from abuses of frequentist testing, including p-hacking, data-dredging, and cherry-picking. It is argued that the metamorphosed PPV misrepresents frequentist testing and misdiagnoses the replication crisis, promoting ill-chosen reforms. The primary source of untrustworthiness is statistical misspecification: invalid probabilistic assumptions imposed on one’s data. This is symptomatic of the much broader problem of the uninformed and recipe-like implementation of frequentist statistics without proper understanding of (a) the invoked probabilistic assumptions and their validity for the data used, (b) the reasoned implementation and interpretation of the inference procedures and their error probabilities, and (c) warranted evidential interpretations of inference results. A case is made that Fisher’s model-based statistics offers a more pertinent and incisive diagnosis of the replication crisis, and provides a well-grounded framework for addressing the issues (a)–(c), which would unriddle the non-replicability/untrustworthiness problems.

Introduced as a complementary concept to Shannon entropy, extropy provides an alternative perspective for measuring uncertainty. While useful in areas such as reliability theory and scoring rules, extropy in its original form treats all outcomes equally, which can limit its applicability in real-world settings where different outcomes have varying degrees of importance. To address this, the weighted extropy measure incorporates a weight function that reflects the relative significance of outcomes, thereby increasing the flexibility and sensitivity of uncertainty quantification. In this paper, we propose a novel recursive non-parametric kernel estimator for weighted extropy based on α-mixing dependent observations, a common setting in time series and stochastic processes. The recursive formulation allows for efficient updating with sequential data, making it particularly suitable for real-time analysis. We establish several theoretical properties of the estimator, including its recursive structure, consistency, and asymptotic behavior under mild regularity conditions. A comprehensive simulation study and data application demonstrate the practical performance of the estimator and validate its superiority over the non-recursive kernel estimator in terms of accuracy and computational efficiency. The results confirm the relevance of the method for dynamic, dependent, and weighted systems.

A smoothed M-estimator is derived from Hampel’s three-part redescending estimator for location and scale. The estimator is shown to be weakly continuous and Fréchet differentiable in the neighbourhood of the normal distribution. Asymptotic assessment is conducted at asymmetric contaminating distributions, where smoothing is shown to improve variance and change-of-variance sensitivity. Other robust metrics compared are largely unchanged, and therefore, the smoothed functions represent an improvement for asymmetric contamination near the rejection point with little downside.

Background: The evolution of “omic” technologies, which measure all biological molecules of a specific type (e.g., genomics), has enabled rapid and cost-effective data acquisition, depending on the technique and sample size. This, however, generates new hurdles that need to be addressed and should be improved upon. This includes selecting the appropriate statistical test based on study design in a high-throughput manner. Methods: An automated statistical analysis pipeline for omic datasets that we coined STATom@ic (pronounced stat-o-matic) was developed in R programming language. Results: We developed an R package that enables statisticians, bioinformaticians, and scientists to perform assumption tests (e.g., normality and variance homogeneity) before selecting appropriate statistical tests. This analysis package can handle two-group and multiple-group comparisons. In addition, this R package can be used for many data formats including normalized counts (RNASeq) and spectral abundance (proteomics and metabolomics). STATom@ic has high precision but lower recall compared to DeSeq2. Conclusions: The STATom@ic R Package is a user-friendly stand-alone or add-on to current bioinformatic workflows that automatically performs appropriate statistical analysis based on the characteristics of the data.

Method comparison studies are typically analyzed using limits of agreement (LoAs). The standard Bland–Altman approach estimates LoAs under the assumption that the differences between methods follow a normal distribution. However, many types of measurements, such as volume, concentration, and percentage values, often deviate from normality. This study explores LoAs for the difference between two clinical measurements and prediction intervals for one measurement given the other, using a transformation of the data. After back-transforming, the resulting LoA for the original measurements depends on the subject level, represented by the average of the measurements. A simulation study evaluates the statistical properties of these LoAs and their confidence limits, demonstrating strong performance for small-to-medium sample sizes. LoA derived from transformed measurements are also compared with those obtained using a regression-based method proposed by Bland and Altman. Two applications demonstrate the approach using logarithmic and cube root transformations. This transformation-based method offers a straightforward way to obtain LoAs that depends on the subject level.

Pre-taxation analysis plays a crucial role in ensuring the fairness of public revenue collection. It can also serve as a tool to reduce the risk of tax avoidance, one of the UK government’s concerns. Our report utilises pre-tax income (PI) and total assets (TA) data from 567 companies listed on the FTSE All-Share index, gathered from the Refinitiv EIKON database, covering 14 years, i.e., the period from 2009 to 2022. We also derive the PI/TA ratio, and distinguish between positive and negative PI cases. We test the conformity of such data to Benford’s Laws, specifically studying the first significant digit (Fd), the second significant digit (Sd), and the first and second significant digits (FSd). We use and justify two pertinent tests, the χ2 and the Mean Absolute Deviation (MAD). We find that both tests do not lead to conclusions in complete agreement with each other—in particular, the MAD test entirely rejects the Benford’s Laws conformity of the reported financial data. From the mere accounting point of view, we conclude that the findings not only cast some doubt on the reported financial data, but also suggest that many more investigations should be considered on closely related matters. On the other hand, the study of a ratio, like PI/TA, of variables that are (or are not) Benford’s Laws-compliant adds to the literature concerning whether such indirect variables should (or should not) be Benford’s Laws-compliant.

Using the China CFPS database, this paper measures the degree of intra-occupational inequality in China with the Pareto coefficient and uses the generalized entropy index to decompose the top income gap by region as well as by industry. The empirical results show that, firstly, the degree of income inequality between occupations in China has increased significantly in recent years. The provinces with a higher degree of income inequality between occupations are mostly located in the more economically developed regions in the central and eastern parts of the country, while the degree of inequality between occupations in the western part is lower. Secondly, the highest-income occupations are mainly in the manufacturing industry, with relatively high levels in the construction industry, the education sector, the wholesale and retail trade, and public administration and social organizations, while the levels in other occupations are relatively low. Lastly, the top income gap primarily originates from within industries. However, the contribution rate of the top income gap between industries is gradually increasing, while the contribution rate of the top income gap within industries is gradually decreasing.