Author(s)

Timur Zubayraev

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Let - be i.i.d. random variables taking values in a measurable space ( Χ, B ). Let φ₁: Χ →□ and φ: Χ²→□ be measurable functions. Assume that φ is symmetric, i.e. φ(x,y)=φ(y.x), for any x,y∈Χ . Consider U-statistic, assuming that Eφ₁(Χ)=0, Eφ(x, X)=0 for all x∈X, Eφ²(x,X)＜∞, Eφ²₁(X)＜∞. We will provide bounds for Δ_N=sup_x|F(x)-F₀(x)-F₁(x)|, where F is a distribution function of T and F₀ , F₁ are its limiting distribution function and Edgeworth correction respectively. Applications of these results are also provided for von Mises statistics case.

U-Statistics, Von Mises Statistics, Symmetric Statistics

Zubayraev, T. (2011) Asymptotic Analysis for U-Statistics and Its Application to Von Mises Statistics. Open Journal of Statistics, 1, 139-144. doi: 10.4236/ojs.2011.13016.