Exponential Probability Inequality for Linearly Negative Quadrant Dependent Random Variables

Ko, Mi-Hwa; Choi, Yang‐Kyu; Choi, Yue-Soon

doi:10.4134/ckms.2007.22.1.137

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Introduction4

P(x < X Y < Y) ≤ P(x < X)p(y < Y)1

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Cited by 14 publications

(11 citation statements)

References 12 publications

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“…Wang and Zhang [3] provided uniform rates of convergence in the central limit theorem for LNQD sequence. Ko and Choi [4] obtained the Hoeffding-type inequality for LNQD sequence. Fu and Wu [5] studied the almost sure central limit theorem for LNQD sequences, and so forth.…”

Section: P(x < X Y < Y) ≤ P(x < X)p(y < Y)mentioning

confidence: 99%

Central limit theorem for stationary linear processes generated by linearly negative quadrant-dependent sequence

2012

J Inequal Appl

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Section: P(x < X Y < Y) ≤ P(x < X)p(y < Y)mentioning

confidence: 99%

Central limit theorem for stationary linear processes generated by linearly negative quadrant-dependent sequence

2012

J Inequal Appl

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“…Wang and Zhang (2006) provided uniform rates of convergence in the central limit theorem for LNQD sequence. Ko, Choi, and Choi (2007) obtained the Hoeffding-type inequality for LNQD sequence. Ko, Ryu, and Kim (2007) studied the strong convergence for weighted sums of LNQD arrays, and so forth.…”

Section: Introductionmentioning

confidence: 98%

Exponential inequalities and complete convergence for a LNQD sequence

Wang

Yang

et al. 2010

Journal of the Korean Statistical Society

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a b s t r a c tSome exponential inequalities for a linearly negative quadrant dependent sequence are obtained. By using the exponential inequalities, we give the complete convergence and almost sure convergence for a linearly negative quadrant dependent sequence. In addition, the asymptotic behavior of the probabilities for the partial sums of a linearly negative quadrant dependent sequence is studied.

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“…Wang and Zhang [8] provided uniform rates of convergence in the central limit theorem for LNQD sequence. Ko et al [2] obtained the Hoeffding-type inequality for LNQD sequence. Ko et al [3] studied the strong convergence for weighted sums of LNQD arrays, Wang et al [7] got the exponential inequalities and complete convergence for a LNQD sequence, Wu et al [9] studied the mean convergence and complete convergence for LNQD sequence, and so forth.…”

Section: Introductionmentioning

confidence: 99%