标题： 矩的评估及其在回归估计中的应用 显示英文标题

标题： Evaluation for moments of a ratio with application to regression estimation

摘要： 随机变量的比率在概率和统计应用中经常出现。 我们旨在在几种依赖性假设下近似这些比率的矩。 扩展Collomb [C. R. Acad. Sci. Paris 285 (1977) 289--292]中的思想，我们提出了随机加权和的矩以及当中心极限定理成立时$L^p$-偏差的更紧的界限。 我们指出在金融和删失数据分析中的适当应用，并专注于功能估计领域的应用。 显示英文摘要

摘要： 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.