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Let {Xj, j ≥ 1} be a strictly stationary φ-mixing sequence of non-degenerate random variables with EX1 = 0. In this paper, we establish a self-normalized weak invariance principle and a central limit theorem for the sequence {Xj} under the condition that L(x) := EX21 I{|X1| ≤ x} is a slowly varying function at ∞, without any higher moment conditions.
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참고문헌 (16)
참고문헌 신청
A. Ra?kauskas / 2001 / Invariance principles for adaptive self-normalized partial sums processes / Stochastic Process. Appl. 95 (1) : 63 ~ 81
M. Csorg? / 1994 / Studentized increments of partial sums / Sci. China Ser. A 37 (3) : 265 ~ 276
M. Csorg? / 2003 / Donsker's theorem for self-normalized partial sums processes / Ann. Probab. 31 (3) : 1228 ~ 1240
M. Peligrad / 1987 / The convergence of moments in the central limit theorem for ρ-mixing sequences of random variables / Proc. Amer. Math. Soc. 101 (1) : 142 ~ 148
M. Peligrad / 1995 / Estimation of the variance of partial sums for ρ-mixing random variables / J. Multivariate Anal. 52 (1) : 140 ~ 157
M. Csorg? / 1994 / Studentized increments of partial sums / Sci. China Ser. A 37 (3) : 265 ~ 276
M. Csorg? / 2003 / Donsker's theorem for self-normalized partial sums processes / Ann. Probab. 31 (3) : 1228 ~ 1240
M. Peligrad / 1987 / The convergence of moments in the central limit theorem for ρ-mixing sequences of random variables / Proc. Amer. Math. Soc. 101 (1) : 142 ~ 148
M. Peligrad / 1995 / Estimation of the variance of partial sums for ρ-mixing random variables / J. Multivariate Anal. 52 (1) : 140 ~ 157
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