Evaluation for moments of a ratio with application to regression estimation

TL;DR

This paper develops methods to approximate moments of ratios of random variables under various dependence conditions, with applications in finance, censored data, and functional estimation.

Contribution

It extends existing bounds for moments of ratios and weighted sums, providing sharper estimates and practical applications in statistical and financial contexts.

Findings

Derived sharper bounds for moments of ratios

Provided applications in finance and censored data analysis

Focused on functional estimation applications

Abstract

Ratios of random variables often appear in probability and statistical applications. We aim to approximate the moments of such ratios under several dependence assumptions. Extending the ideas in Collomb [C. R. Acad. Sci. Paris 285 (1977) 289--292], we propose sharper bounds for the moments of randomly weighted sums and for the $L^p$-deviations from the asymptotic normal law when the central limit theorem holds. We indicate suitable applications in finance and censored data analysis and focus on the applications in the field of functional estimation.