Abstract
Let {X n ; n ≥ 1} be a sequence of independent and identically distributed U[0,1]-distributed random variables. Define the uniform empirical process \(F_n (t) = n^{ - \tfrac{1} {2}} \sum\nolimits_{i = 1}^n {(I_{\{ X_i \leqslant t\} } - t),0} \leqslant t \leqslant 1,\left\| {F_n } \right\| = \sup _{0 \leqslant t \leqslant 1} \left| {F_n (t)} \right| \). In this paper, the exact convergence rates of a general law of weighted infinite series of E {‖F n ‖ − ɛg s(n)}+ are obtained.
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Supported by National Natural Science Foundation of China (Grant No. 10901138), National Science Fundation of Zhejiang Province (Grant No. R6090034) and the Young Excellent Talent Foundation of Huaiyin Normal University
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Zang, Q.P., Huang, W. A general law of moment convergence rates for uniform empirical process. Acta. Math. Sin.-English Ser. 27, 1941–1948 (2011). https://doi.org/10.1007/s10114-011-9752-0
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DOI: https://doi.org/10.1007/s10114-011-9752-0