2025/03/28 by Frédéric Ferraty, Han Lin Shang, Ferraty, Frédéric +1
Computer Science · Mathematics · Social Sciences · #62P25 #62R10 #Applications (stat.AP) #Bayesian Methods and Mixture Models #FOS: Computer and information sciences #Insurance, Mortality, Demography, Risk Management #Methodology (stat.ME) #Statistical Methods and Inference
paper · pdf · doi:10.48550/arxiv.2503.22904
openalex publication_date 2025/03/28 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
This paper is concerned with forecasting probability density functions. Density functions are nonnegative and have a constrained integral; thus, they do not constitute a vector space. Implementing unconstrained functional time-series forecasting methods is problematic for such nonlinear and constrained data. A novel forecasting method is developed based on a nonparametric function-on-function regression, where both the response and the predictor are probability density functions. Asymptotic properties of our nonparametric regression estimator are established, as well as its finite-sample performance through a series of Monte-Carlo simulation studies. Using COVID-19 data from the French department and age-specific period life tables from the United States, we assess and compare the finite-sample forecast accuracy of the proposed method with several existing methods.