Total variation bounds in the Lindeberg central limit theorem

2025/11/04 by Dung, N. T., Thao, H. T. P.
Mathematics · Decision Sciences · #Random Matrices and Applications #Probability and Risk Models #Advanced Harmonic Analysis Research

paper · doi:10.48550/arxiv.2511.02391

Abstract

In this paper, we obtain an explicit total variation bound in the central limit theorem for the sums of non-i.i.d. random variables. Our results show that, under suitable assumptions, Lindeberg's condition is sufficient and necessary for the convergence in total variation distance.

Citations

• Fisher-type information involving higher order derivatives
• Rates of Fisher information convergence in the central limit theorem for nonlinear statistics
• Stein's method for comparison of univariate distributions
• Fisher information and the central limit theorem
• Berry-Esseen bounds in the entropic central limit theorem

Related

• Approximate central limit theorems
• Lindeberg's method for moderate deviations and random summation
• Total variation estimates in the Breuer-Major theorem
• Stable central limit theorem in total variation distance
• An Invariance Principle for Stochastic Series II. Non Gaussian Limits