Estimates of the Difference of Two Distribution Functions

Zhengyan Lin () and Zhidong Bai ()
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Zhengyan Lin: Zhejiang University, Department of Mathematics
Zhidong Bai: Northeast Normal University, School of Mathematics and Statistics

Chapter Chapter 4 in Probability Inequalities, 2010, pp 29-36 from Springer

Abstract: Abstract Rates of weak convergence are important for application of weak limit theorems. Thus, investigation on convergence rates has been an active research topic for decades. Generally speaking, the convergence rates are established by various basic inequalities between two distribution functions and/or functions of bounded variation in terms of various transformations. The first work was done be Berry-Esseen who established the convergence rate of normal approximation in terms of Fourier transformations or characteristic functions. Stein and Chen created a new method to evaluate the convergence rates of normal or Poisson approximation for non-independent sums. In 1993, Bai established convergence rates of empirical spectral distributions of large dimensional random matrices in terms of Stieltjes transforms. In this chapter, we only introduce some basic inequalities of difference of two distribution functions. Their applications can be found in (1995), (1986) and (1993).

Keywords: Convergence Rate; Central Limit Theorem; Bounded Variation; Poisson Approximation; Edgeworth Expansion (search for similar items in EconPapers)
Date: 2010
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Persistent link: https://EconPapers.repec.org/RePEc:spr:sprchp:978-3-642-05261-3_4

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DOI: 10.1007/978-3-642-05261-3_4

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