2022/10/19 by Zhaoyang Shi, Krishnakumar Balasubramanian, Shi, Zhaoyang +3
Economics, Econometrics and Finance · Mathematics · #FOS: Computer and information sciences #FOS: Mathematics #Machine Learning (stat.ML) #Mathematical Dynamics and Fractals #Point processes and geometric inequalities #Probability (math.PR) #Statistics Theory (math.ST) #Stochastic processes and financial applications
paper · pdf · doi:10.48550/arxiv.2210.10744
openalex publication_date 2022/10/19 · openalex created_date 2023/02/11 · openalex updated_date 2026/07/28
We derive normal approximation results for a class of stabilizing functionals of binomial or Poisson point process, that are not necessarily expressible as sums of certain score functions. Our approach is based on a flexible notion of the add-one cost operator, which helps one to deal with the second-order cost operator via suitably appropriate first-order operators. We combine this flexible notion with the theory of strong stabilization to establish our results. We illustrate the applicability of our results by establishing normal approximation results for certain geometric and topological statistics arising frequently in practice. Several existing results also emerge as special cases of our approach.