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Forecasting in probabilistic time series is a complex endeavor that extends beyond predicting future values to also quantifying the uncertainty inherent in these predictions. Gaussian process regression stands out as a Bayesian machine…

We consider kernel estimation of marginal densities and regression functions of stationary processes. It is shown that for a wide class of time series, with proper centering and scaling, the maximum deviations of kernel density and…

Statistics Theory · Mathematics 2010-10-21 Weidong Liu , Wei Biao Wu

We consider a semiparametric generalized linear model and study estimation of both marginal and quantile effects in this model. We propose an approximate maximum likelihood estimator, and rigorously establish the consistency, the asymptotic…

Methodology · Statistics 2022-04-06 Seong-ho Lee , Yanyuan Ma , Elvezio Ronchetti

Quantile regression (QR) is a principal regression method for analyzing the impact of covariates on outcomes. The impact is described by the conditional quantile function and its functionals. In this paper we develop the nonparametric…

In this paper we introduce a kernel-based measure for detecting differences between two conditional distributions. Using the `kernel trick' and nearest-neighbor graphs, we propose a consistent estimate of this measure which can be computed…

Methodology · Statistics 2024-08-30 Anirban Chatterjee , Ziang Niu , Bhaswar B. Bhattacharya

Prediction is a key issue in time series analysis. Just as classical mean regression models, classical autoregressive methods, yielding L$^2$ point-predictions, provide rather poor predictive summaries; a much more informative approach is…

Statistics Theory · Mathematics 2025-10-06 Alberto González-Sanz , Marc Hallin , Yisha Yao

The Sustainable Development Goals (SDGs) of the United Nations consist of 17 general objectives, subdivided into 169 targets to be achieved by 2030. Several SDG indices and indicators require continuous analysis and evaluation, and most of…

Methodology · Statistics 2025-08-26 João Inácio Scrimini , Cleber Bisognin , Renata Rojas Guerra , Fábio M. Bayer

In this work, we propose a novel deep bootstrap framework for nonparametric regression based on conditional diffusion models. Specifically, we construct a conditional diffusion model to learn the distribution of the response variable given…

Machine Learning · Statistics 2026-02-12 Jinyuan Chang , Yuling Jiao , Lican Kang , Junjie Shi

This article introduces a novel dynamic framework to Bayesian model averaging for time-varying parameter quantile regressions. By employing sequential Markov chain Monte Carlo, we combine empirical estimates derived from dynamically chosen…

Statistics Theory · Mathematics 2024-11-08 Mauro Bernardi , Roberto Casarin , Bertrand Maillet , Lea Petrella

Many scientific problems involve data exhibiting both temporal and cross-sectional dependencies. While linear dependencies have been extensively studied, the theoretical analysis of regression estimators under nonlinear dependencies remains…

Statistics Theory · Mathematics 2025-02-27 Marie-Christine Düker , Adam Waterbury

Crop yield is affected by various soil and environmental parameters and can vary significantly. Therefore, a crop yield estimation model which can predict pre-harvest yield is required for food security. The study is conducted on tea forms…

Machine Learning · Computer Science 2025-12-30 Nisar Ahmed , Hafiz Muhammad Shahzad Asif , Gulshan Saleem , Muhammad Usman Younus

We consider a Bayesian method for simultaneous quantile regression on a real variable. By monotone transformation, we can make both the response variable and the predictor variable take values in the unit interval. A representation of…

Methodology · Statistics 2018-11-08 Priyam Das , Subhashis Ghoshal

Deep nonparametric regression, characterized by the utilization of deep neural networks to learn target functions, has emerged as a focus of research attention in recent years. Despite considerable progress in understanding convergence…

Machine Learning · Statistics 2024-08-01 Yuling Jiao , Lican Kang , Jin Liu , Heng Peng , Heng Zuo

R. Tyrell Rockafellar and collaborators introduced, in a series of works, new regression modeling methods based on the notion of superquantile (or conditional value-at-risk). These methods have been influential in economics, finance,…

Optimization and Control · Mathematics 2022-01-04 Yassine Laguel , Krishna Pillutla , Jérôme Malick , Zaid Harchaoui

In a classical regression model, it is usually assumed that the explanatory variables are independent of each other and error terms are normally distributed. But when these assumptions are not met, situations like the error terms are not…

Statistics Theory · Mathematics 2017-09-08 Bahadır Yüzbaşı , Yasin Asar , Ahmet Demiralp , M. Şamil Şık

In using multiple regression methods for prediction, one often considers the linear combination of explanatory variables as an index. Seeking a single such index when here are multiple responses is rather more complicated. One classical…

Methodology · Statistics 2020-11-19 Stephen Portnoy , Joseph Haimberg

Quantile Factor Models (QFM) represent a new class of factor models for high-dimensional panel data. Unlike Approximate Factor Models (AFM), where only location-shifting factors can be extracted, QFM also allow to recover unobserved factors…

Econometrics · Economics 2020-09-24 Liang Chen , Juan Jose Dolado , Jesus Gonzalo

The purpose of this paper relies on the study of long term yield curves modeling. Inspired by the economic litterature, it provides a financial interpretation of the Ramsey rule that links discount rate and marginal utility of aggregate…

Computational Finance · Quantitative Finance 2014-04-08 Nicole El Karoui , Caroline Hillairet , Mohamed Mrad

Growth charts are often more informative when they are customized per subject, taking into account prior measurements and possibly other covariates of the subject. We study a global semiparametric quantile regression model that has the…

Statistics Theory · Mathematics 2007-06-13 Ying Wei , Xuming He

This paper develops theory for feasible estimators of finite-dimensional parameters identified by general conditional quantile restrictions, under much weaker assumptions than previously seen in the literature. This includes instrumental…

Statistics Theory · Mathematics 2021-10-07 Luciano de Castro , Antonio F. Galvao , David M. Kaplan , Xin Liu