• Title/Summary/Keyword: negatively orthant dependent

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On the Negative Quadrant Dependence in Three Dimensions

  • Ko, Mi-Hwa;Kim, Tae-Sung
    • Honam Mathematical Journal
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    • v.25 no.1
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    • pp.117-127
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    • 2003
  • In this note we perform an extreme point analysis on two natural definitions of negative quadrant dependence of three random variables and examine how different these two notions of dependence. We also characterize some special distributions which are both negatively lower orthant dependent and negatively upper orthant dependent.

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STRONG LIMIT THEOREMS FOR WEIGHTED SUMS OF NOD SEQUENCE AND EXPONENTIAL INEQUALITIES

  • Wang, Xuejun;Hu, Shuhe;Volodin, Andrei I.
    • Bulletin of the Korean Mathematical Society
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    • v.48 no.5
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    • pp.923-938
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    • 2011
  • Some properties for negatively orthant dependent sequence are discussed. Some strong limit results for the weighted sums are obtained, which generalize the corresponding results for independent sequence and negatively associated sequence. At last, exponential inequalities for negatively orthant dependent sequence are presented.

ALMOST SURE AND COMPLETE CONSISTENCY OF THE ESTIMATOR IN NONPARAMETRIC REGRESSION MODEL FOR NEGATIVELY ORTHANT DEPENDENT RANDOM VARIABLES

  • Ding, Liwang
    • Bulletin of the Korean Mathematical Society
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    • v.57 no.1
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    • pp.51-68
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    • 2020
  • In this paper, the author considers the nonparametric regression model with negatively orthant dependent random variables. The wavelet procedures are developed to estimate the regression function. For the wavelet estimator of unknown function g(·), the almost sure consistency is derived and the complete consistency is established under the mild conditions. Our results generalize and improve some known ones for independent random variables and dependent random variables.

A NOTE ON COMPLETE MOMENT CONVERGENCE FOR ARRAYS OF ROWWISE EXTENDED NEGATIVELY ORTHANT DEPENDENT RANDOM VARIABLES

  • Kim, Hyun-Chull
    • Journal of the Chungcheong Mathematical Society
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    • v.25 no.3
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    • pp.507-519
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    • 2012
  • In this paper we obtain the complete moment convergence for an array of rowwise extended negative orthant dependent random variables. By using the result we can prove the complete moment convergence for some positively orthant dependent sequence satisfying the extended negative orthant dependence.

EQUIVALENT CONDITIONS OF COMPLETE MOMENT CONVERGENCE AND COMPLETE INTEGRAL CONVERGENCE FOR NOD SEQUENCES

  • Deng, Xin;Wang, Xuejun
    • Bulletin of the Korean Mathematical Society
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    • v.54 no.3
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    • pp.917-933
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    • 2017
  • In this paper, seven equivalent conditions of complete moment convergence and complete integral convergence for negatively orthant dependent (NOD, in short) sequences are shown under two cases: identical distribution and stochastic domination. The results obtained in the paper improve and generalize the corresponding ones of Liang et al. [10]). In addition, an extension of the Baum-Katz complete convergence theorem: six equivalent conditions of complete convergence is established.

STRONG LAWS OF LARGE NUMBERS FOR WEIGHTED SUMS OF NEGATIVELY DEPENDENT RANDOM VARIABLES

  • Ko, Mi-Hwa;Han, Kwang-Hee;Kim, Tae-Sung
    • Journal of the Korean Mathematical Society
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    • v.43 no.6
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    • pp.1325-1338
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    • 2006
  • For double arrays of constants ${a_{ni},\;1{\leq}i{\leq}k_n,\;n{\geq}1}$ and sequences of negatively orthant dependent random variables ${X_n,\;n{\geq}1}$, the conditions for strong law of large number of ${\sum}^{k_n}_{i=1}a_{ni}X_i$ are given. Both cases $k_n{\uparrow}{\infty}\;and\;k_n={\infty}$ are treated.