scholarly journals Remarks on uniform convergence of random variables and statistics

2012 ◽  
Vol 45 (2) ◽  
Author(s):  
Wojciech Niemiro ◽  
Ryszard Zieliński
Keyword(s):  
Uniform Convergence ◽  
Random Variables ◽  
Convergence In Distribution ◽  
Convergence Almost Surely

AbstractConvergence in distribution, convergece in probability, and convergence almost surely,

scholarly journals Precise Asymptotics in the Law of the Iterated Logarithm under Sublinear Expectations

2021 ◽  
Vol 2021 ◽  
pp. 1-9
Author(s):  
Mingzhou Xu ◽  
Kun Cheng
Keyword(s):  
Central Limit Theorem ◽  
Limit Theorem ◽  
Uniform Convergence ◽  
Central Limit ◽  
Random Variables ◽  
Precise Asymptotics ◽  
Partial Sum ◽  
The Central Limit Theorem ◽  
Iterated Logarithm ◽  
The Law

By an inequality of partial sum and uniform convergence of the central limit theorem under sublinear expectations, we establish precise asymptotics in the law of the iterated logarithm for independent and identically distributed random variables under sublinear expectations.

Convergence of Complex Uncertain Double Sequences

2020 ◽  
Vol 16 (03) ◽  
pp. 447-459 ◽  
Author(s):  
Debasish Datta ◽  
Binod Chandra Tripathy
Keyword(s):  
Complex Numbers ◽  
Convergence In Distribution ◽  
Double Sequences ◽  
Convergence In Measure ◽  
Uncertain Variables ◽  
Mean Convergence ◽  
Model Complex ◽  
Uncertainty Space ◽  
Convergence Almost Surely ◽  
Convergence In Mean

Complex uncertain variables are measurable functions from an uncertainty space to the set of complex numbers and are used to model complex uncertain quantities. This paper introduces the convergence concepts of convergence almost surely (a.s.), convergence in measure, convergence in mean, convergence in distribution and convergence uniformly almost surely complex uncertain double sequences. In addition, relationships among the introduced classes of sequences have been introduced.

scholarly journals From convergence in distribution to uniform convergence

2016 ◽  
Vol 22 (2) ◽  
pp. 695-710 ◽  
Author(s):  
J. M. Bogoya ◽  
A. Böttcher ◽  
E. A. Maximenko
Keyword(s):  
Uniform Convergence ◽  
Convergence In Distribution

scholarly journals Generic Uniform Convergence

1992 ◽  
Vol 8 (2) ◽  
pp. 241-257 ◽  
Author(s):  
Donald W.K. Andrews
Keyword(s):  
Uniform Convergence ◽  
Asymptotic Properties ◽  
Convergence In Probability ◽  
Test Statistics ◽  
Parameter Spaces ◽  
Totally Bounded ◽  
Convergence Results ◽  
Large Numbers ◽  
Uniform Law ◽  
Convergence Almost Surely

This paper presents several generic uniform convergence results that include generic uniform laws of large numbers. These results provide conditions under which pointwise convergence almost surely or in probability can be strengthened to uniform convergence. The results are useful for establishing asymptotic properties of estimators and test statistics.The results given here have the following attributes, (1) they extendresults of Newey to cover convergence almost surely as well as convergence in probability, (2) they apply to totally bounded parameter spaces (rather than just to compact parameter spaces), (3) they introduce a set of conditions for a generic uniform law of large numbers that has the attribute of giving the weakest conditions available for i.i.d. contexts, but which apply in some dependent nonidentically distributed contexts as well, and (4) they incorporate and extend themain results in the literature in a parsimonious fashion.

scholarly journals HUBUNGAN ANTARA KONVERGEN HAMPIR PASTI, KONVERGEN DALAM PELUANG, DAN KONVERGEN DALAM SEBARAN

2013 ◽  
Vol 2 (2) ◽  
pp. 10
Author(s):  
Vira Agusta ◽  
Dodi Devianto ◽  
Hazmira Yozza
Keyword(s):  
Probability Space ◽  
Random Variable ◽  
Convergence In Probability ◽  
Convergence In Distribution ◽  
Convergence Almost Surely ◽  
The Relationship

Let fXng be a sequence of random variable dened on a probability space ( ; F; P). In this paper, we studied about the relationship between the convergence almost surely, convergence in probability, and convergence in distribution. If the sequenceof random variable convergence almost surely to a random variable X then fXng convergence in probability to X. If the sequence of random variable fXng convergence in probability to a random variable X then fXng convergence in distribution to X.

Convergence in distribution for randomly stopped random fields

2021 ◽  
Vol 105 (0) ◽  
pp. 137-149
Author(s):  
D. Silvestrov
Keyword(s):  
Random Field ◽  
Random Fields ◽  
Metric Spaces ◽  
Random Variables ◽  
Random Variable ◽  
Convergence In Distribution ◽  
Content Type ◽  
General Conditions

Let X \mathbb {X} and Y \mathbb {Y} be two complete, separable, metric spaces, ξ ε ( x ) , x ∈ X \xi _\varepsilon (x), x \in \mathbb {X} and ν ε \nu _\varepsilon be, for every ε ∈ [ 0 , 1 ] \varepsilon \in [0, 1] , respectively, a random field taking values in space Y \mathbb {Y} and a random variable taking values in space X \mathbb {X} . We present general conditions for convergence in distribution for random variables ξ ε ( ν ε ) \xi _\varepsilon (\nu _\varepsilon ) that is the conditions insuring holding of relation, ξ ε ( ν ε ) ⟶ d ξ 0 ( ν 0 ) \xi _\varepsilon (\nu _\varepsilon ) \stackrel {\mathsf {d}}{\longrightarrow } \xi _0(\nu _0) as ε → 0 \varepsilon \to 0 .

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