scholarly journals Almost Sure Central Limit Theory for Self-Normalized Products of Sums of Partial Sums

2012 ◽  
Vol 2012 ◽  
pp. 1-13
Author(s):  
Qunying Wu
Keyword(s):  
Limit Theorem ◽  
Central Limit ◽  
Random Variables ◽  
Domain Of Attraction ◽  
The Self ◽  
Partial Sums ◽  
Limit Theory ◽  
Almost Sure Limit Theorem ◽  
Products Of Sums ◽  
Normal Law

LetX,X1,X2,…be a sequence of independent and identically distributed random variables in the domain of attraction of a normal law. An almost sure limit theorem for the self-normalized products of sums of partial sums is established.

scholarly journals A Beveridge–Nelson filters for the self normalization

2021 ◽  
Vol 47 ◽  
Author(s):  
Mindaugas Juodis
Keyword(s):  
Central Limit Theorem ◽  
Limit Theorem ◽  
Central Limit ◽  
Domain Of Attraction ◽  
Linear Process ◽  
Sum Of Squares ◽  
The Self ◽  
Infinite Variance ◽  
Normal Law

Let Xt =Σ∞i=0 ψi εt−i be a linear process, where εt , t ∈ Z, are i.i.d. r.v.’s in the domain of attraction of a normal law with zero mean and possibly infinite variance. Generalizing the class of Beveridge–Nelson filters this article proves a central limit theorem for the self-normalized sums U−1n Σnt=1 Xt , where U2n is a sum of squares of block-sums of size m, as m and the number of blocks N = n/m tend to infinity.

ASYMPTOTIC BEHAVIOR OF TRIMMED SUMS

2012 ◽  
Vol 12 (01) ◽  
pp. 1150002 ◽  
Author(s):  
ISTVÁN BERKES ◽  
LAJOS HORVÁTH ◽  
JOHANNES SCHAUER
Keyword(s):  
Asymptotic Behavior ◽  
Central Limit ◽  
Random Variables ◽  
Domain Of Attraction ◽  
Independent Random Variables ◽  
Partial Sums ◽  
Stable Law ◽  
Limit Theory ◽  
Trimmed Sums ◽  
The Central Limit Theorem

Trimming is a standard method to decrease the effect of large sample elements in statistical procedures, used, e.g., for constructing robust estimators. It is also a powerful tool in understanding deeper properties of partial sums of independent random variables. In this paper we review some basic results of the theory and discuss new results in the central limit theory of trimmed sums. In particular, we show that for random variables in the domain of attraction of a stable law with parameter 0 < α < 2, the asymptotic behavior of modulus trimmed sums depends sensitively on the number of elements eliminated from the sample. We also show that under moderate trimming, the central limit theorem always holds if we allow random centering factors. Finally, we give an application to change point problems.

scholarly journals Almost sure central limit theorem for self-normalized partial sums of negatively associated random variables

Filomat ◽  
2017 ◽  
Vol 31 (5) ◽  
pp. 1413-1422 ◽  
Author(s):  
Qunying Wu ◽  
Yuanying Jiang
Keyword(s):  
Central Limit Theorem ◽  
Limit Theorem ◽  
Central Limit ◽  
Random Variables ◽  
Stationary Sequence ◽  
The Self ◽  
Partial Sums ◽  
Associated Random Variables ◽  
Negatively Associated ◽  
Negatively Associated Random Variables

Let X,X1,X2,... be a stationary sequence of negatively associated random variables. A universal result in almost sure central limit theorem for the self-normalized partial sums Sn/Vn is established, where: Sn = ?ni=1 Xi,V2n = ?ni=1 X2i .

scholarly journals An expansion related to the central limit theorem

1969 ◽  
Vol 10 (1-2) ◽  
pp. 219-230
Author(s):  
C. R. Heathcote
Keyword(s):  
Central Limit Theorem ◽  
Limit Theorem ◽  
Central Limit ◽  
Random Variables ◽  
Partial Sums ◽  
The Central Limit Theorem ◽  
Independent And Identically Distributed

Let X1, X2,…be independent and identically distributed non-lattice random variables with zero, varianceσ2<∞, and partial sums Sn = X1+X2+…+X.

scholarly journals On Feller's criterion for the law of the iterated logarithm

1994 ◽  
Vol 17 (2) ◽  
pp. 323-340 ◽  
Author(s):  
Deli Li ◽  
M. Bhaskara Rao ◽  
Xiangchen Wang
Keyword(s):  
Central Limit Theorem ◽  
Limit Theorem ◽  
Central Limit ◽  
Uniform Estimate ◽  
Random Variables ◽  
Independent Random Variables ◽  
Partial Sums ◽  
The Central Limit Theorem ◽  
Iterated Logarithm ◽  
The Law

Combining Feller's criterion with a non-uniform estimate result in the context of the Central Limit Theorem for partial sums of independent random variables, we obtain several results on the Law of the Iterated Logarithm. Two of these results refine corresponding results of Wittmann (1985) and Egorov (1971). In addition, these results are compared with the corresponding results of Teicher (1974), Tomkins (1983) and Tomkins (1990)

Almost sure limit theorems for random allocations

2005 ◽  
Vol 42 (2) ◽  
pp. 173-194
Author(s):  
István Fazekas ◽  
Alexey Chuprunov
Keyword(s):  
Central Limit Theorem ◽  
Limit Theorem ◽  
Central Limit ◽  
Limit Theorems ◽  
Random Variables ◽  
Central Domain ◽  
Almost Sure Limit Theorem ◽  
The Central Limit Theorem ◽  
Almost Sure Limit Theorems ◽  
Poisson Limit

Almost sure limit theorems are presented for random allocations. A general almost sure limit theorem is proved for arrays of random variables. It is applied to obtain almost sure versions of the central limit theorem for the number of empty boxes when the parameters are in the central domain. Almost sure versions of the Poisson limit theorem in the left domain are also proved.

Sign in / Sign up

Export Citation Format

Share Document