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Let {X, X_n; nge 1} be a sequence of i.i.d. randomvariables which belong to the attraction of the normal law, andX_n^{(1)}, ldots, X_n^{(n)} be an arrangement of X_1, ldots,X_n in decreasing order of magnitude, i.e., |X_n^{(1)}|gecdots ge |X_n^{(n)}|. Suppose that {r_n} is a sequence ofconstants satisfying some mild conditions and d^{'}(t_{n_k}) isan appropriate truncation level, where n_k=[beta^k] and betais any constant larger than one. Then we show that theconditionally trimmed sums obeys the self-normalized law of theiterated logarithm (LIL). Moreover, the self-normalized LIL for
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참고문헌 (13)
참고문헌 신청
/ 1968. / An Introduction to Probability and ItsApplications. Vol. I
/ 1975 / Limit theorems on the self-normalizedrange for weakly and strongly dependent processes 31 : 271 ~
/ 1988 / Non-classical law of the iteratedlogarithm behaviour for trimmed sums 78 (2) : 293 ~
/ 1988 / Universal asymptotic normality forconditionally trimmed sums 7 (1) : 9 ~
/ 1989 / Self-normalized laws ofthe iterated logarithm 17 (4) : 1571 ~
/ 1975 / Limit theorems on the self-normalizedrange for weakly and strongly dependent processes 31 : 271 ~
/ 1988 / Non-classical law of the iteratedlogarithm behaviour for trimmed sums 78 (2) : 293 ~
/ 1988 / Universal asymptotic normality forconditionally trimmed sums 7 (1) : 9 ~
/ 1989 / Self-normalized laws ofthe iterated logarithm 17 (4) : 1571 ~
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