# SELF-NORMALIZED WEAK LIMIT THEOREMS FOR A ø-MIXING SEQUENCE

• Choi, Yong-Kab (DEPARTMENTS OF MATHEMATICS AND RINS GYEONGSANG NATIONAL UNIVERSITY) ;
• Moon, Hee-Jin (DEPARTMENTS OF MATHEMATICS AND RINS GYEONGSANG NATIONAL UNIVERSITY)
• Published : 2010.11.30
• 56 6

#### Abstract

Let {$X_j,\;j\geq1$} be a strictly stationary $\phi$-mixing sequence of non-degenerate random variables with $EX_1$ = 0. In this paper, we establish a self-normalized weak invariance principle and a central limit theorem for the sequence {$X_j$} under the condition that L(x) := $EX_1^2I{|X_1|{\leq}x}$ is a slowly varying function at $\infty$, without any higher moment conditions.

#### Keywords

self-normalized random variables;invariance principle;central limit theorem;mixing sequence

#### Acknowledgement

Supported by : NRF

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#### Cited by

1. A self-normalized central limit theorem for a ρ-mixing stationary sequence 2017, https://doi.org/10.1080/03610926.2016.1277754
2. A self-normalized invariance principle for a ϕ-mixing sequence vol.66, pp.2, 2013, https://doi.org/10.1007/s10998-013-7100-0