Further Results on the Limiting Distribution of GMM Sample Moment Conditions

For a sequence of independent, identically distributed random variable (iid rv's) [Formula: see text] and a sequence of integer-valued random variables [Formula: see text], define the random quantiles as [Formula: see text], where [Formula: see text] denote the largest integer less than or equal to [Formula: see text], and [Formula: see text] the [Formula: see text]th order statistic in a sample [Formula: see text] and [Formula: see text]. In this note, the limiting distribution and its exact order approximation are obtained for [Formula: see text]. The limiting distribution result we obtain extends the work of several including Wretman[Formula: see text]. The exact order of normal approximation generalizes the fixed sample size results of Reiss[Formula: see text]. AMS 2000 subject classification: 60F12; 60F05; 62G30.

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The geometricity of the limiting distributions in queues and dams

Journal of Applied Probability ◽

10.1017/s0021900200117449 ◽

1993 ◽

Vol 30 (02) ◽

pp. 438-445

Author(s):

R. M. Phatarfod

Keyword(s):

Random Walks ◽

Limiting Distribution ◽

Duality Relation ◽

Limiting Distributions ◽

Initial Term

There are a number of cases in the theories of queues and dams where the limiting distribution of the pertinent processes is geometric with a modified initial term — herein called zero-modified geometric (ZMG). The paper gives a unified treatment of the various cases considered hitherto and some others by using a duality relation between random walks with impenetrable and with absorbing barriers, and deriving the probabilities of absorption by using Waldian identities. Thus the method enables us to distinguish between those cases where the limiting distribution would be ZMG and those where it would not.

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QuickSort: Improved right-tail asymptotics for the limiting distribution, and large deviations (Extended Abstract)

2019 Proceedings of the Sixteenth Workshop on Analytic Algorithmics and Combinatorics (ANALCO) ◽

10.1137/1.9781611975505.9 ◽

2019 ◽

pp. 87-93

Author(s):

James Allen Fill ◽

Wei-Chun Hung

Keyword(s):

Large Deviations ◽

Limiting Distribution ◽

Tail Asymptotics

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Complete convergence for sums of arrays of random elements

International Journal of Mathematics and Mathematical Sciences ◽

10.1155/s0161171200003112 ◽

2000 ◽

Vol 23 (11) ◽

pp. 789-794 ◽

Cited By ~ 2

Author(s):

Soo Hak Sung

Keyword(s):

Complete Convergence ◽

Moment Conditions ◽

Random Elements ◽

Rowwise Independent

Let{Xni}be an array of rowwise independentB-valued random elements and{an}constants such that0<an↑∞. Under some moment conditions for the array, it is shown that∑i=1nXni/anconverges to0completely if and only if∑i=1nXni/anconverges to0in probability.

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