Evaluation for moments of a ratio with application to regression estimation

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 application in finance and censored data analysis and focus on the applications in the field of functional estimation