scholarly journals Rates of strong convergence for U-statistics in finite populations

1991 ◽  
Vol 50 (3) ◽  
pp. 468-480
Author(s):  
P. N. Kokic ◽  
N. C. Weber
Keyword(s):  
Strong Convergence ◽  
Random Sample ◽  
Finite Population ◽  
Random Variables ◽  
Rates Of Convergence ◽  
Simple Random Sample ◽  
Finite Populations ◽  
Strong Law ◽  
U Statistics ◽  
Convergence Results

AbstractLet UNn be a U-statistic based on a simple random sample of size n selected without replacement from a finite population of size N. Rates of convergence results in the strong law are obtained for UNn, which are similar to those known for classical U-statistics based on samples of independent and identically distributed (iid) random variables.

A martingale approach to strong convergence of the number of records

2001 ◽  
Vol 33 (4) ◽  
pp. 864-873 ◽  
Author(s):  
Raúl Gouet ◽  
F. Javier López ◽  
Miguel San Miguel
Keyword(s):  
Distribution Function ◽  
Strong Convergence ◽  
Wide Class ◽  
Random Variables ◽  
Strong Law ◽  
Martingale Approach ◽  
Common Distribution ◽  
Common Distribution Function ◽  
Independent Identically Distributed

Let (Xn) be a sequence of independent, identically distributed random variables, with common distribution function F, possibly discontinuous. We use martingale arguments to connect the number of upper records from (Xn) with sums of minima of related random variables. From this relationship we derive a general strong law for the number of records for a wide class of distributions F, including geometric and Poisson.

A martingale approach to strong convergence of the number of records

2001 ◽  
Vol 33 (04) ◽  
pp. 864-873 ◽  
Author(s):  
Raúl Gouet ◽  
F. Javier López ◽  
Miguel San Miguel
Keyword(s):  
Distribution Function ◽  
Strong Convergence ◽  
Wide Class ◽  
Random Variables ◽  
Strong Law ◽  
Martingale Approach ◽  
Common Distribution ◽  
Common Distribution Function ◽  
Independent Identically Distributed

Let (X n ) be a sequence of independent, identically distributed random variables, with common distribution function F, possibly discontinuous. We use martingale arguments to connect the number of upper records from (X n ) with sums of minima of related random variables. From this relationship we derive a general strong law for the number of records for a wide class of distributions F, including geometric and Poisson.

Approximations to extreme tail probabilities for sampling without replacement

1969 ◽  
Vol 66 (3) ◽  
pp. 587-606 ◽  
Author(s):  
M. Stone
Keyword(s):  
Random Sample ◽  
Normal Approximation ◽  
Random Variables ◽  
Tail Probability ◽  
Random Permutation ◽  
Simple Random Sample ◽  
Tail Probabilities ◽  
Asymptotically Normal ◽  
Sampling Fraction ◽  
Image Position

Introduction and summary: In the distribution of the sum of n random variablesfor which we suppose , the tail probability will be called an extreme tail probability if the normal approximationis poor, when is asymptotically normal and n is large. This paper concerns the specialization of (1.1) in whichwith a random permutation of nλ ones and n − nλ zeros, that is, in which T is the total for a simple random sample from the population with sampling fraction λ. In this case, we will always write T as Tλ. For brevity, we may write {c1,…, cn} for .

scholarly journals Complete convergence for weighted sums of widely orthant-dependent random variables

2021 ◽  
Vol 2021 (1) ◽  
Author(s):  
Pingyan Chen ◽  
Soo Hak Sung
Keyword(s):  
Complete Convergence ◽  
Law Of Large Numbers ◽  
Random Variables ◽  
Weighted Sums ◽  
Dependent Random Variables ◽  
Strong Law ◽  
Link Type ◽  
Convergence Results ◽  
Large Numbers ◽  
Widely Orthant Dependent

AbstractThe complete convergence results for weighted sums of widely orthant-dependent random variables are obtained. A strong law of large numbers for weighted sums of widely orthant-dependent random variables is also obtained. Our results extend and generalize some results of Chen and Sung (J. Inequal. Appl. 2018:121, 2018), Zhang et al. (J. Math. Inequal. 12:1063–1074, 2018), Chen and Sung (Stat. Probab. Lett. 154:108544, 2019), Lang et al. (Rev. Mat. Complut., 2020, 10.1007/s13163-020-00369-5), and Liang (Stat. Probab. Lett. 48:317–325, 2000).

scholarly journals On Strong Convergence for Weighted Sums of a Class of Random Variables

2013 ◽  
Vol 2013 ◽  
pp. 1-7 ◽  
Author(s):  
Aiting Shen
Keyword(s):  
Strong Convergence ◽  
Complete Convergence ◽  
Law Of Large Numbers ◽  
Random Variables ◽  
Maximal Inequality ◽  
Weighted Sums ◽  
Moment Condition ◽  
Strong Law ◽  
Linear Statistics ◽  
Large Numbers

Let{Xn,n≥1}be a sequence of random variables satisfying the Rosenthal-type maximal inequality. Complete convergence is studied for linear statistics that are weighted sums of identically distributed random variables under a suitable moment condition. As an application, the Marcinkiewicz-Zygmund-type strong law of large numbers is obtained. Our result generalizes the corresponding one of Zhou et al. (2011) and improves the corresponding one of Wang et al. (2011, 2012).

scholarly journals On strong convergence of arrays

1994 ◽  
Vol 50 (2) ◽  
pp. 219-223 ◽  
Author(s):  
Yong-Cheng Qi
Keyword(s):  
Strong Convergence ◽  
Random Variables ◽  
Almost Sure Convergence ◽  
Strong Law ◽  
Iterated Logarithm ◽  
The Law ◽  
Independent And Identically Distributed

In this paper we study almost sure convergence for arrays of independent and identically distributed random variables. We obtain a condition under which Marcinkiewicz's strong law holds and get a rate analogous to the law of the iterated logarithm under a condition weaker than Hu and Weber's.

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