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U statistic functions for a class of Edgeworth expansion

,MAC Cosmetics sale, X2), K3 one. {Eg. (1) +3 Eg (x1) g (2) (z1, 2)}, K a {Eg4 (1) a 3 +12 Eg (1) g (z2) (l, z2) +12 Eg (x) g (2 ) (1, z.) ~ o (x2, x3)}, 1 a C2C1 (a 2C +2 OfFz a 3C} a 4C2). Cl A,ed hardy danmark, cz one. Card: The f (U) Third Taglor start: Because f (U) A () + P () (a) + (I). + Ji () (u I). + To the factory . / c, () (a) - in case of a feed material and because P {IR1 ≥} a P {(【, a) 22aI ≥ garlic (1ognJl ≤ 1) {C. I-o (n (3-2 ) (3-3) again by Lemma [2] and formula (3-2), formula (3-3) know that only permits: + materials 3) - N (x) I = 0 (4iEY a Xn, c a gg, √ ... one by (iii) known, f ()()> o. so it can be written as: spy + cy: + czy a 3f () 2f () 2 'a cz Temple ≤. Bu Ⅳ czl a .5 (a) When lI1, the first discussion of seeking a solution set of inequality Cubic: y: + C1Y + C2Y a C2 ÷ 3E ()] was established under: the type (3-5) in (3-5) is the same solution with the following inequality equation (3-5) with Inequality: {x ≤ Grade + sound. + corpse s () 0 ()). where P () for a 18 degree polynomial. by (3-5) know that only permits: corpse First + sound xa4-P18 (x ) O (n-2)) ... · 6 Lemma [2] that x ≤ + other + a2x34-Pl ~ (x) O (n2)) of a guitar [such as c eleven BU () [a a2x2 + K2 + la, K + (3 ~ 3) + (5-1.. +15)] I () [Ji aK3X2 (2-1) 一号 a]}} a 。().( 3-7) from (3 -6) (3-7) have: a1 eleven K, a one t. into (3-7) body {≤) - N (x) .8 (b) when ≤ a time, similar to the proof of Theorem 2 license: supl Ⅳ () l A. (n1) · use of Lemma 3: I {x a corpse + x: + j2, f, (3-4) know: body {≤) - N (x) .9 (c) ≥ time when a similar license, (3-4) also set up. General (a), (b),ed hardy shop, (c) Code King Single 3 available [1] [2] [3] 【Reference】 GHOSHM.Berry-EsseenBoundforfunctionalsofU-statisticsEJJ.San-Khya, l985 ,47:255-270. Kang Min Qi. U statistic is the function and VonMises statistics self-help (Bootstrap) and random weighting approximation [J]. Mathematical Statistics and Applied Probability, 1988,3 (2) :192-204. CAIIAERTH, VERERBEKEN.TheorderofthenormalapproximationforaStudentizedUStatistics [J]. AnnStatist,ed hardy mexico, l98l, 9: l94-200. [ ,],[4): l463-1484. [6] Chen Xi Ru. VonMises on u statistics and statistics of the limit properties [J]. Science, 1980 (6) :522-532.

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