A Comparison Theorem on Moment Inequalities Between Negatively Associated and Independent Random Variables

By Qi-Man Shao. 2000

357 citations recorded by the source corpus.

Subfields: Applied Mathematics, Management Science and Operations Research, Statistics and Probability

View Paper: https://www.semanticscholar.org/paper/16a75f343bbfc12df9d0921c4bbebb6a8eb65b9d

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In Applied Mathematics

In Management Science and Operations Research

In Statistics and Probability

Citations in the corpus

On complete convergence in Marcinkiewicz-Zygmund type SLLN for negatively associated random variables (2010, background): “In our further considerations we need the following lemmas. Lemma 1.1 (Shao [ 11 ]).”
Probability and moment inequalities under dependence (2013, methodology): “Under various types of strong mixing conditions, the Rosenthal type inequalities have been obtained for dependent random variables; see Shao (1988, 1995, 2000), Peligrad (1985, 1989), Utev and Peligrad (2003), and Rio (2000).”
Determinantal probability measures (2002, background): “ are known to hold for negatively associated random variables, especially for a stationary collection of negatively random variables indexed by Zd. For example, see Newman (1984), Shao and Su (1999), Shao (2000), Zhang and Wen (2001), Zhang (2001), and the references therein. We shall merely state o”
Precise large deviations for sums of random variables with consistently varying tails (2004, background): “For details of the notion of NA, please refer to Alam and Saxena (1981), Joag-Dev and Proschan (1983) and Shao (2000), among others.”
Rosenthal’s inequalities for independent and negatively dependent random variables under sub-linear expectations with applications (2014, background): “For moment inequalities of partial sums of the classical negatively dependent random variables and related strong limit theorems, one can refer to Shao (2000), Su, Zhao and Wang (1997), Yuan and An (2009), Zhang (2000, 2001a, 2001b), Zhang and Wen (2001) etc.”
Complete moment and integral convergence for sums of negatively associated random variables (2008, background): “Some references for these NA counterparts are listed as follows: • Central Limit Theorem (Newman [12], Roussas [13], Su and Chi [14]) • Three-Series Criterion (Matula [15]) • Weak Law of Large Numbers (Chi and Su [16]) • Moment Inequalities (Su, Zhao, and Wang [17], Liu, Gan, and Chen [18], Shao [ 1”
Maximal Moment Inequality for Partial Sums of Strong Mixing Sequences and Application (2007, unknown): “One can refer to Billingsley (1968, [1]), Peligrad (1982, 1985, 1987, [2–4]), Roussas and Ioannides (1987, [5]), Shao (1988, 1989, 1995, [6–8]), Yang (1997, [9]) and Zhang (1998, 2000, [10, 11]) for φ-mixing or ρ-mixing sequences, Birkel (1988, [12]) and Shao and Yu (1996, [13]) for positively assoc”
Strong Limit Theorems for Weighted Sums of Negatively Associated Random Variables (2008, background): “Lemma 4.1 (Shao [ 34 ]) Let {Xi, 1 ≤ i ≤ n} be a sequence of NA r.v.’s with zero means and finite second moments.”
Rosenthal type inequalities for asymptotically almost negatively associated random variables and applications (2009, methodology): “The following Rosenthal type inequalities for AANA random variables extend the corresponding results for NA random variables, see for example, Theorem 2 of [ 8 ] or Theorem 1 of [6].”
Strong approximation for a class of stationary processes (2009, background): “The following Fuk–Nagaev inequality can be found in [27].”
Negative association, ordering and convergence of resampling methods (2017, methodology): “The SSP resampling scheme ρssp : [0, 1] N × Z → Pf (X ) is based on the Srinivasan’s (2001) randomized rounding technique (also known as pivotal sampling in the sampling survey literature, see e.”
Probability inequalities for END sequence and their applications (2011, unknown): “Shao [6]).”
Complete convergence for weighted sums of NSD random variables and its application in the EV regression model (2014, methodology): “This lemma can be proved by the comparison theorem on moments between the NSD random variables and independent random variables (see Hu 2000), following the similar process of Theorem 3 in Shao (2000).”
On the strong convergence rate for weighted sums of arrays of rowwise negatively orthant dependent random variables (2013, unknown): “3 [16].”
The Weak Convergence for Functions of Negatively Associated Random Variables (2001, unknown): “See Su et al. (1997) or Shao (2000).”
Exponential probability inequalities for WNOD random variables and their applications (2016, unknown): “Shao [15]) For any x ≥ 0, ln(1 + x) ≥ x 1 + x + x2 2(1 + x)2 [ 1 + 2 3 ln(1 + x) ] .”