ResearchTrend.AI
  • Papers
  • Communities
  • Events
  • Blog
  • Pricing
Papers
Communities
Social Events
Terms and Conditions
Pricing
Parameter LabParameter LabTwitterGitHubLinkedInBlueskyYoutube

© 2025 ResearchTrend.AI, All rights reserved.

  1. Home
  2. Papers
  3. 2403.14032
15
0

Large parameter asymptotic analysis for homogeneous normalized random measures with independent increments

20 March 2024
Chi Yan
Shui Feng
Yaozhong Hu
ArXivPDFHTML
Abstract

Homogeneous normalized random measures with independent increments (hNRMIs) represent a broad class of Bayesian nonparametric priors and thus are widely used. In this paper, we obtain the strong law of large numbers, the central limit theorem and the functional central limit theorem of hNRMIs when the concentration parameter aaa approaches infinity. To quantify the convergence rate of the obtained central limit theorem, we further study the Berry-Esseen bound, which turns out to be of the form O(1a)O \left( \frac{1}{\sqrt{a}}\right)O(a​1​). As an application of the central limit theorem, we present the functional delta method, which can be employed to obtain the limit of the quantile process of hNRMIs. As an illustration of the central limit theorems, we demonstrate the convergence numerically for the Dirichlet processes and the normalized inverse Gaussian processes with various choices of the concentration parameters.

View on arXiv
Comments on this paper