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Evaluation for moments of a ratio with application to regression estimation. (English) Zbl 1200.62035

Summary: 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 ideas of G. Collomb [C. R. Acad. Sci., Paris, Sér. A 285, 289–292 (1977; Zbl 0375.62042)], 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.

MSC:

62G08 Nonparametric regression and quantile regression
62M09 Non-Markovian processes: estimation
60F05 Central limit and other weak theorems

Citations:

Zbl 0375.62042
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References:

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