Model-Based and Model-Free point prediction algorithms for locally stationary random fields

Srinjoy Das; Yiwen Zhang; Dimitris N. Politis

Home/Archive/arXiv

arXiv · 2212.03079

Model-Based and Model-Free point prediction algorithms for locally stationary random fields

Srinjoy Das·Yiwen Zhang·Dimitris N. Politis

View original source ↗Read source document ↗Export metadata ↓

Abstract

The Model-free Prediction Principle has been successfully applied to general regression problems, as well as problems involving stationary and locally stationary time series. In this paper we demonstrate how Model-Free Prediction can be applied to handle random fields that are only locally stationary, i.e., they can be assumed to be stationary only across a limited part over their entire region of definition. We construct one-step-ahead point predictors and compare the performance of Model-free to Model-based prediction using models that incorporate a trend and/or heteroscedasticity. Both aspects of the paper, Model-free and Model-based, are novel in the context of random fields that are locally (but not globally) stationary. We demonstrate the application of our Model-based and Model-free point prediction methods to synthetic data as well as images from the CIFAR-10 dataset and in the latter case show that our best Model-free point prediction results outperform those obtained using Model-based prediction.

Explore related subjects

stat.ME

Keep this discovery

Explore connections, maps & timelines

BibTeX RIS

Srinjoy Das, Yiwen Zhang, Dimitris N. Politis. 2022-12-06. Model-Based and Model-Free point prediction algorithms for locally stationary random fields. https://arxiv.org/abs/2212.03079

Cite the original work for its findings. Save a collection to share your selection of sources.

KEEP EXPLORING

Related papers

arXiv2026

Modeling cyclostationarity in time series using ASCA

Modern data analysis across diverse disciplines increasingly relies on time series. Many of these datasets exhibit cyclostationarity, where patterns approximately repeat in a regular manner, often across multiple time scales, such as daily, weekly or yearly cycles. In this context, statistical inference is essential to distinguish genuine underlying effects from random variability. While tools like Analysis of Variance (ANOVA) provide such inference, they often lack interpretability and struggle with the complexities of multivariate data. To address these limitations, we propose a unified pipeline for the exploratory analysis of cyclostationary times series using ANOVA Simultaneous Component Analysis (ASCA). ASCA is an extension of ANOVA that is able to work in both univariate and multivariate cases. Combining inference with the visualization capabilities of Principal Component Analysis (PCA), ASCA provides powerful options for interpretability. ASCA's capabilities have been well-established in the analysis of experimental data, but they remain largely unexplored for observational data like time series. Our workflow introduces an algorithmic approach to modeling time-dependent data using ASCA, enabling control over multiple cyclostationary time scales while also accounting for the specific challenges of this type of data, such as autocorrelation. Furthermore, we observed that ASCA provides a better separation of variability across factors than ANOVA in unbalanced designs due to its multivariate nature. We demonstrate the efficacy of this methodology through two real-world case studies: water temperature trends in mountain lakes in Sierra Nevada, Spain, and airborne pollen trends over 30 years recorded in the city of Granada, Spain.

stat.ME↗

arXiv2026

Distributionally balanced sampling designs via tactical configurations

Distributionally balanced sampling designs are low-discrepancy probability designs obtained by minimizing the expected discrepancy between the auxiliary-variable distribution of a random sample and the target population distribution. Existing constructions rely on circular population sequences, which restrict the design space by forcing samples to be contiguous blocks of a sequence. We propose a new construction based on tactical configurations that removes this topological constraint. The resulting designs are fixed-size and have equal inclusion probabilities. We develop both a simple initialization valid for arbitrary population and sample sizes and a spatial initialization that yields a lower initial expected discrepancy, together with a simulated annealing algorithm for optimization within this class. In simulations and empirical examples, the proposed method outperforms state-of-the-art alternatives in terms of distributional fit and balance.

stat.ME↗

arXiv2026

Bayesian Quantile Regression for Misclassified Binary Data with an Application to Spousal Violence Reporting

Survey responses on socially undesirable behaviors, such as self-reported spousal violence, are often subject to underreporting due to social stigma, fear of retaliation, and other reporting pressures. When such data are analyzed using standard econometric models that focus on conditional means, such as probit and logit models, the resulting estimates are likely to be biased and can obscure heterogeneity in covariate effects. To address these challenges, we propose a Bayesian binary quantile regression framework that accounts for misclassification and provides quantile-specific effects for the latent true response. The framework incorporates false-negative and false-positive probabilities to capture reporting errors and employs a novel partially collapsed Gibbs sampler for estimation. We also discuss the computation of covariate effects and marginal likelihood for Bayesian model comparison. Simulation studies under various settings (prior effective sample size, misclassification rates, and prior distribution) show that accounting for misclassification improves inference across quantiles relative to models that ignore reporting errors. We apply the framework to women's self-reported spousal violence and find that underreporting of spousal violence exceeds overreporting across quantiles, while model comparisons using marginal likelihood generally favor the quantile model with misclassification and yield different conclusions about the determinants of reported violence.

stat.ME↗