### Citations

5185 | Convergence of Probability Measures - BILLINGSLEY - 1968 |

220 |
Some concepts of dependence
- Lehmann
- 1966
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Citation Context ..., g(X j : j ∈ A2) } ≤ 0, whenever f and g are coordinatewise nondecreasing such that this covariance exists. An infinite sequence {Xn| n ≥ 1} is NA if every finite subcollection is NA. Definition 2. (=-=Lehmann, 1966-=-) Two random variables X and Y are said to be negative quadrant dependent(NQD) if for any x, y ∈ R, P (X < x,Y < y) ≤ P(X < x)P(Y < y). A sequence {Xn|n ≥ 1} of random variables is said to be pairwise... |

93 | Complete convergence and the law of large numbers - Hsu, Robbins - 1947 |

68 |
Asymptotic independence and limit theorems for positive and negatively dependent random variables,
- Newman
- 1984
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Citation Context ...random variables, then (a) EXY ≤ EXEY, (b) P(X < x, Y < y) ≤ P(X < x)P(Y < y), and (c) If f and g are both nondecreasing (or both nonincreasing) functions, then f (X) and g(Y) are NQD. Definition 3. (=-=Newman, 1984-=-) A sequence {Xn|n ≥ 1} of random variables is said to be linearly negative quadrant dependent(LNQD) if for any disjoint subsets A, B ⊂ N+ and positive r j′s,∑ k∈A rkXk and ∑ j∈B r jX j are NQD. Lemma... |

10 |
Complete convergence for arrays
- Gut
- 1992
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Citation Context ... expected value if the variance of the summands is finite. This result has been generalized and extended in several directions and carefully studied by many authors (see, Pruitt, 1966; Rohatgi, 1971; =-=Gut, 1992-=-; Wang et al., 1993; Kuczmaszewska and Szynal, 1994; Magda and Sergey, 1997; Ghosal and Chandra, 1998; Hu et al., 1999, 2001; Antonini et al., 2001; Ahmed et al., 2002; Liang et al., 2004; Baek et al.... |

10 |
On complete convergence for arrays of rowwise independent random elements in Banach spaces. Stochastic Anal
- Hu, Rosalsky, et al.
- 1999
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Citation Context ...ral directions and carefully studied by many authors (see, Pruitt, 1966; Rohatgi, 1971; Gut, 1992; Wang et al., 1993; Kuczmaszewska and Szynal, 1994; Magda and Sergey, 1997; Ghosal and Chandra, 1998; =-=Hu et al., 1999-=-, 2001; Antonini et al., 2001; Ahmed et al., 2002; Liang et al., 2004; Baek et al., 2005). Antonini et al. (2001) obtained result of the following theorem on complete and they had established some res... |

10 |
Summability of independent random variables
- Pruitt
- 1966
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Citation Context ...s converges completely to the expected value if the variance of the summands is finite. This result has been generalized and extended in several directions and carefully studied by many authors (see, =-=Pruitt, 1966-=-; Rohatgi, 1971; Gut, 1992; Wang et al., 1993; Kuczmaszewska and Szynal, 1994; Magda and Sergey, 1997; Ghosal and Chandra, 1998; Hu et al., 1999, 2001; Antonini et al., 2001; Ahmed et al., 2002; Liang... |

7 |
Convergence of weighted sums of independent random variables
- Rohatgi
- 1971
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Citation Context ...mpletely to the expected value if the variance of the summands is finite. This result has been generalized and extended in several directions and carefully studied by many authors (see, Pruitt, 1966; =-=Rohatgi, 1971-=-; Gut, 1992; Wang et al., 1993; Kuczmaszewska and Szynal, 1994; Magda and Sergey, 1997; Ghosal and Chandra, 1998; Hu et al., 1999, 2001; Antonini et al., 2001; Ahmed et al., 2002; Liang et al., 2004; ... |

6 | On complete convergence in a Banach space
- Kuczmaszewska, Szynal
- 1994
(Show Context)
Citation Context ...e of the summands is finite. This result has been generalized and extended in several directions and carefully studied by many authors (see, Pruitt, 1966; Rohatgi, 1971; Gut, 1992; Wang et al., 1993; =-=Kuczmaszewska and Szynal, 1994-=-; Magda and Sergey, 1997; Ghosal and Chandra, 1998; Hu et al., 1999, 2001; Antonini et al., 2001; Ahmed et al., 2002; Liang et al., 2004; Baek et al., 2005). Antonini et al. (2001) obtained result of ... |

5 |
On complete convergence for weighted sums of arrays of Banach space valued random elements with application to moving average processes
- Ahmed, Antonini, et al.
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Citation Context ...uthors (see, Pruitt, 1966; Rohatgi, 1971; Gut, 1992; Wang et al., 1993; Kuczmaszewska and Szynal, 1994; Magda and Sergey, 1997; Ghosal and Chandra, 1998; Hu et al., 1999, 2001; Antonini et al., 2001; =-=Ahmed et al., 2002-=-; Liang et al., 2004; Baek et al., 2005). Antonini et al. (2001) obtained result of the following theorem on complete and they had established some results for independent and identically distributed ... |

5 |
Convergence of weighted sums for dependent random variables
- Liang, Zhang, et al.
- 2004
(Show Context)
Citation Context ... 1966; Rohatgi, 1971; Gut, 1992; Wang et al., 1993; Kuczmaszewska and Szynal, 1994; Magda and Sergey, 1997; Ghosal and Chandra, 1998; Hu et al., 1999, 2001; Antonini et al., 2001; Ahmed et al., 2002; =-=Liang et al., 2004-=-; Baek et al., 2005). Antonini et al. (2001) obtained result of the following theorem on complete and they had established some results for independent and identically distributed random variables. Th... |

5 | Convergence rates on strong laws of large numbers for arrays of rowwise independent elements. Stochastic Anal
- Wang, Rao, et al.
- 1993
(Show Context)
Citation Context ...alue if the variance of the summands is finite. This result has been generalized and extended in several directions and carefully studied by many authors (see, Pruitt, 1966; Rohatgi, 1971; Gut, 1992; =-=Wang et al., 1993-=-; Kuczmaszewska and Szynal, 1994; Magda and Sergey, 1997; Ghosal and Chandra, 1998; Hu et al., 1999, 2001; Antonini et al., 2001; Ahmed et al., 2002; Liang et al., 2004; Baek et al., 2005). Antonini e... |

4 |
Smooth estimate of quantiles under association,”
- Cai, Roussas
- 1997
(Show Context)
Citation Context ...-Il Baek Newman (1984) introduced the concepts of LNQD r.v.’s. Many authors derived several important properties about LNQD random variables and also discussed some applications in several areas (see =-=Cai and Roussas, 1997-=-; Wang and Zhang, 2006; Ko et al., 2007 among others). Throughout this paper, a = O(b) means that there exists some constant C > 0 such that a ≤ Cb. 2. Main Results Theorem 2. Let {Xni|1 ≤ i ≤ n, n ≥ ... |

4 | On the rate of complete convergence for weighted sums of arrays of Banach-space-valued random elements, Theory Probab. - Hu, Li, et al. - 2002 |

4 |
A Berry-Esseen theorem for weakly negatively dependent random variables and its applications,”
- Wang, Zhang
- 2006
(Show Context)
Citation Context ...introduced the concepts of LNQD r.v.’s. Many authors derived several important properties about LNQD random variables and also discussed some applications in several areas (see Cai and Roussas, 1997; =-=Wang and Zhang, 2006-=-; Ko et al., 2007 among others). Throughout this paper, a = O(b) means that there exists some constant C > 0 such that a ≤ Cb. 2. Main Results Theorem 2. Let {Xni|1 ≤ i ≤ n, n ≥ 1} be an array of roww... |

3 |
Complete convergence of martingale arrays
- Ghosal, Chandra
- 1998
(Show Context)
Citation Context ...lized and extended in several directions and carefully studied by many authors (see, Pruitt, 1966; Rohatgi, 1971; Gut, 1992; Wang et al., 1993; Kuczmaszewska and Szynal, 1994; Magda and Sergey, 1997; =-=Ghosal and Chandra, 1998-=-; Hu et al., 1999, 2001; Antonini et al., 2001; Ahmed et al., 2002; Liang et al., 2004; Baek et al., 2005). Antonini et al. (2001) obtained result of the following theorem on complete and they had est... |

3 | negative association of random variables, with applications. - Dev, Proschan - 1983 |

2 |
Limiting behaviors of weighted sums for linearly negative quadrant dependent random variables,”
- Ko, Ryu, et al.
- 2007
(Show Context)
Citation Context ...s of LNQD r.v.’s. Many authors derived several important properties about LNQD random variables and also discussed some applications in several areas (see Cai and Roussas, 1997; Wang and Zhang, 2006; =-=Ko et al., 2007-=- among others). Throughout this paper, a = O(b) means that there exists some constant C > 0 such that a ≤ Cb. 2. Main Results Theorem 2. Let {Xni|1 ≤ i ≤ n, n ≥ 1} be an array of rowwise LNQD random v... |

1 |
On the strong convergence of weighted sums, Stochastic Analysis and Applications
- Antonini, Kwon, et al.
- 2001
(Show Context)
Citation Context ...fully studied by many authors (see, Pruitt, 1966; Rohatgi, 1971; Gut, 1992; Wang et al., 1993; Kuczmaszewska and Szynal, 1994; Magda and Sergey, 1997; Ghosal and Chandra, 1998; Hu et al., 1999, 2001; =-=Antonini et al., 2001-=-; Ahmed et al., 2002; Liang et al., 2004; Baek et al., 2005). Antonini et al. (2001) obtained result of the following theorem on complete and they had established some results for independent and iden... |

1 |
On the complete convergence of weighted sums for dependent random variables
- Baek, Park, et al.
- 2005
(Show Context)
Citation Context ...; Gut, 1992; Wang et al., 1993; Kuczmaszewska and Szynal, 1994; Magda and Sergey, 1997; Ghosal and Chandra, 1998; Hu et al., 1999, 2001; Antonini et al., 2001; Ahmed et al., 2002; Liang et al., 2004; =-=Baek et al., 2005-=-). Antonini et al. (2001) obtained result of the following theorem on complete and they had established some results for independent and identically distributed random variables. Theorem 1. Let {Xn|n ... |

1 |
Central limit theorem for linear processes, The Annals of Probability
- Magda, Sergey
- 1997
(Show Context)
Citation Context ...s result has been generalized and extended in several directions and carefully studied by many authors (see, Pruitt, 1966; Rohatgi, 1971; Gut, 1992; Wang et al., 1993; Kuczmaszewska and Szynal, 1994; =-=Magda and Sergey, 1997-=-; Ghosal and Chandra, 1998; Hu et al., 1999, 2001; Antonini et al., 2001; Ahmed et al., 2002; Liang et al., 2004; Baek et al., 2005). Antonini et al. (2001) obtained result of the following theorem on... |