2022/08/05 by Sujay Bhatt, Bhatt, Sujay, Guanhua Fang +5 · 1 citation
Decision Sciences · Economics, Econometrics and Finance · #FOS: Computer and information sciences #FOS: Mathematics #Financial Risk and Volatility Modeling #Machine Learning (cs.LG) #Machine Learning (stat.ML) #Probability and Risk Models #Statistics Theory (math.ST) #Stochastic processes and financial applications
paper · pdf · doi:10.48550/arxiv.2208.03185
openalex publication_date 2022/08/05 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
In this paper, we provide an extension of confidence sequences for settings where the variance of the data-generating distribution does not exist or is infinite. Confidence sequences furnish confidence intervals that are valid at arbitrary data-dependent stopping times, naturally having a wide range of applications. We first establish a lower bound for the width of the Catoni-style confidence sequences for the finite variance case to highlight the looseness of the existing results. Next, we derive tight Catoni-style confidence sequences for data distributions having a relaxed bounded~pth-moment, where~p ∈ (1,2], and strengthen the results for the finite variance case of~p =2. The derived results are shown to better than confidence sequences obtained using Dubins-Savage inequality.