Abstract
In this chapter we shall discuss the classical scheme of sums of independent random variables, which will allow us to sharpen many of the previous results. In particular, the logarithmic factor appearing in the bounds for the Kolmogorov distance in Propositions 17.1.1 and 17.5.1 may be removed (as well as in the deviation bound of Proposition 17.6.1). This is shown using Fourier Analysis, more precisely – a third order Edgeworth expansion for characteristic functions under the 4-th moment condition (cf. Chapter 4), and applying several results from Chapter 10 about deviations of elementary polynomials on the unit sphere. Even better bounds hold when applying a fourth order Edgeworth expansion under the 5-th moment condition.
| Original language | English (US) |
|---|---|
| Title of host publication | Probability Theory and Stochastic Modelling |
| Publisher | Springer Nature |
| Pages | 389-409 |
| Number of pages | 21 |
| DOIs | |
| State | Published - 2023 |
Publication series
| Name | Probability Theory and Stochastic Modelling |
|---|---|
| Volume | 104 |
| ISSN (Print) | 2199-3130 |
| ISSN (Electronic) | 2199-3149 |
Bibliographical note
Publisher Copyright:© 2023, The Author(s), under exclusive license to Springer Nature Switzerland AG.