  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.
