In this study, we propose the use of the concentration function as a novel tool for assessing the adequacy of predictive distributions in a Bayesian framework. The methodology relies on a rolling-origin evaluation strategy, in which the available time series is partitioned into two segments: the first is used for model estimation, while the second is used for out-of-sample prediction. The concentration function is then constructed for each set of forecasts, providing a distributional assessment of predictive performance across competing models. In this framework, the model with the least inequality in its concentration function is interpreted as offering superior predictive fit. To complement this curve-based analysis, we compute two well-established inequality measures-the Gini concentration coefficient and the Pietra index-which provide further evidence and consistency regarding model performance. These measures allow for a comprehensive evaluation of how closely predictive distributions align with observed outcomes. The proposed methodology is validated through a simulation study, in which its ability to discriminate between models is assessed under controlled conditions. We illustrate its practical applicability by analyzing real-world data, thus demonstrating the usefulness of concentration functions and associated inequality measures as diagnostic tools for Bayesian predictive evaluation.
A class of exchangeable multivariate max-id distributions with 1-norm pound symmetric exponent measure was introduced by Genest, Neslehova and Rivest in a paper published in the journal Bernoulli in 2018. Three years later, an extended class of exchangeable multivariate max-id distributions with p-norm pound symmetric exponent measure was proposed by Mai and Wang in an article which appeared in the Journal of Multivariate Analysis. A new class is proposed here which encompasses them both and which allows for non-exchangeability, thereby providing extra flexibility for modeling multivariate block maxima data and extreme risks. Some properties of members of this class are studied, and conditions are given under which they are multivariate extreme-value distributions. The maximum attractor of each class member is also determined under broad conditions, and an algorithm due to Jan-Frederik Mai is adapted for simulation purposes.
We study early warning of short-horizon volatility spikes by combining three complementary blocks of information: functional data analysis summaries based on functional principal component analysis scores and derivative norms, multi-scale topological data analysis descriptors derived from persistent homology, and heterogeneous autoregressive lagged-volatility features. All models are trained under a strict chronological design, with operating thresholds pre-specified from out-of-fold scores to ensure that model selection and evaluation remain separate. Statistical significance is assessed using paired DeLong tests for the receiver operating characteristic area under the curve and is complemented by a calendar block bootstrap that more directly accounts for temporal dependence in the scores. Across four large-capitalization equities (INTC, COP, NVDA, DIS), the combined specification (BOTH, defined as functional data analysis features plus topological data analysis features plus heterogeneous autoregressive features) generally outperforms the functional data analysis-only and topological data analysis-only baselines in receiver operating characteristic area under the curve and precision-recall area under the curve, and improves their probabilistic accuracy and calibration while remaining competitive with a heterogeneous autoregressive-only gradient-boosted tree benchmark. In a regime-switching generalized autoregressive conditional heteroskedasticity stress experiment, a heterogeneous autoregressive-based gradient-boosted tree model attains the highest discrimination, illustrating that the empirical gains from combining functional and topological information are not guaranteed when the data-generating mechanism is close to a low-dimensional lag-volatility structure. Methodologically, we propose a time-respecting method that integrates functional and topological geometry with paired inference under temporal dependence. Practically, we provide a reproducible script for early warning and for monitoring short-run volatility stress.
We develop a new method based on the Lq-likelihood to perform robust covariance estimation on spatial data. We propose the maximum composite Lq-likelihood estimator (MCLqE), which is obtained from a combination of the maximum Lq-likelihood and the composite likelihood. In order to down-weight a single value at a spatial location, we make use of the composite likelihood of the spatial data, which is in the form of the product of the pairwise likelihood of all pairs of the observations. We apply the maximum Lq-likelihood on each pair to form the MCLqE, which effectively down-weights abnormal observations in a spatial dataset and gives more robust covariance parameter estimation results when the data are contaminated by outliers. We adapt the hyperparameter tuning procedure developed for the MLqE to the new MCLqE framework. The robustness of the MCLqE is further verified by both simulation studies and experiments on a precipitation dataset from the US.
Reliable quantification of treatment benefit in late-phase clinical trials increasingly requires modeling patient histories that include progression, adverse events, and treatment switches. Conventional multi-state analyses often invoke the Markov property and assume independent right censoring-conditions rarely satisfied in oncology, immunology, or cell-therapy programs, where intermediate events and informative dropout are common. This article presents a systematic review and bibliometric synthesis of 48 peer-reviewed studies published through 11 June 2025 that (i) relax the Markov assumption and (ii) address complex observation schemes such as left truncation, interval censoring, or informative censoring, identified through Web of Science and Scopus searches following preferred reporting items for systematic reviews and meta-analyses 2020 guidelines.A recurring set of methodological strategies emerges across the literature, including semi-Markov transition-intensity models, illness-death and semi-competing risks frameworks, landmarking for dynamic prediction, and inverse-probability-of-censoring weighting. Estimation approaches range from nonparametric product integrals to semiparametric weighted likelihoods and Bayesian Markov chain Monte Carlo, with recent contributions exploring saddle-point approximations and subsampling for large-scale electronic health records. To complement this synthesis, we include a compact simulation contrasting baseline and landmark Aalen-Johansen estimators under semi-Markov dynamics with history-dependent censoring, and a bibliometric network analysis mapping collaboration patterns, thematic clusters, and structural gaps. The findings highlight the need for scalable, auditable software, robust diagnostics aligned with the International Council for Harmonization E9(R1) estimand framework (which links clinical trial objectives to precise statistical targets), and better integration of high-dimensional biomarkers; limitations include the English-language restriction and reliance on bibliometric meta-data. Addressing these priorities may enhance both the methodological robustness and regulatory applicability of non-Markov survival models.
