Asymptotic Expansions for the Distributions of Canonical $V$-Statistics of Third Order
Igor' Semenovich Borisov, Nadezhda Vladimirovna Volod'ko · Theory of Probability and Its Applications · 2016
The second term of the Edgeworth-type asymptotic expansion is obtained for the distribution function of a canonical $V$-statistic of order three, based on samples from the sequence of independent identically distributed variables. Under minimal moment restrictions, the remainder term has the optimal order $O(n^{-1})$.