Almost sure convergence of weighted sums

Xiru Chen; Lixing Zhu; Kai Tai Fang

Almost sure convergence of weighted sums

Xiru Chen, Lixing Zhu, Kai Tai Fang

Department of Mathematics

Research output: Contribution to journal › Journal article › peer-review

11 Citations (Scopus)

Abstract

Suppose that e₁,e₂,... are i.i.d. random variables with Ee₁ = 0 and E|e₁|^r < ∞ for some r with 1 ≤ r < 2. In this paper, we obtain sufficient conditions for almost sure convergence of the weighted sum ∑_i=1ⁿ a(i)e_i/A(n) and derive that these conditions are necessary in some sense.

Original language	English
Pages (from-to)	499-507
Number of pages	9
Journal	Statistica Sinica
Volume	6
Issue number	2
Publication status	Published - Apr 1996

Scopus Subject Areas

Statistics and Probability
Statistics, Probability and Uncertainty

User-Defined Keywords

Almost sure convergence
Consistency
Linear regression

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http://www3.stat.sinica.edu.tw/statistica/oldpdf/A6n214.pdf

Cite this

@article{ecb744efb4bf409e87873a65177f66b6,

title = "Almost sure convergence of weighted sums",

abstract = "Suppose that e1,e2,... are i.i.d. random variables with Ee1 = 0 and E|e1|r < ∞ for some r with 1 ≤ r < 2. In this paper, we obtain sufficient conditions for almost sure convergence of the weighted sum ∑i=1n a(i)ei/A(n) and derive that these conditions are necessary in some sense.",

keywords = "Almost sure convergence, Consistency, Linear regression",

author = "Xiru Chen and Lixing Zhu and Fang, {Kai Tai}",

note = "The first two authors received support from the NNSF of China, Hong Kong UPGC grant, and the Statistics Research and Consultancy Unit, Hong Kong Baptist University. The last author was partly supported by a Hong Kong UPGC grant. The authors are grateful to the referees and Editors for their valuable suggestions which were helpful for improving the presentation of the paper.",

year = "1996",

month = apr,

language = "English",

volume = "6",

pages = "499--507",

journal = "Statistica Sinica",

issn = "1017-0405",

publisher = "Institute of Statistical Science",

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TY - JOUR

T1 - Almost sure convergence of weighted sums

AU - Chen, Xiru

AU - Zhu, Lixing

AU - Fang, Kai Tai

N1 - The first two authors received support from the NNSF of China, Hong Kong UPGC grant, and the Statistics Research and Consultancy Unit, Hong Kong Baptist University. The last author was partly supported by a Hong Kong UPGC grant. The authors are grateful to the referees and Editors for their valuable suggestions which were helpful for improving the presentation of the paper.

PY - 1996/4

Y1 - 1996/4

N2 - Suppose that e1,e2,... are i.i.d. random variables with Ee1 = 0 and E|e1|r < ∞ for some r with 1 ≤ r < 2. In this paper, we obtain sufficient conditions for almost sure convergence of the weighted sum ∑i=1n a(i)ei/A(n) and derive that these conditions are necessary in some sense.

AB - Suppose that e1,e2,... are i.i.d. random variables with Ee1 = 0 and E|e1|r < ∞ for some r with 1 ≤ r < 2. In this paper, we obtain sufficient conditions for almost sure convergence of the weighted sum ∑i=1n a(i)ei/A(n) and derive that these conditions are necessary in some sense.

KW - Almost sure convergence

KW - Consistency

KW - Linear regression

UR - http://www3.stat.sinica.edu.tw/statistica/j6n2/j6n214/j6n214.htm

UR - https://www.jstor.org/stable/24306031

UR - http://www.scopus.com/inward/record.url?scp=21344435912&partnerID=8YFLogxK

M3 - Journal article

AN - SCOPUS:21344435912

SN - 1017-0405

VL - 6

SP - 499

EP - 507

JO - Statistica Sinica

JF - Statistica Sinica

IS - 2

ER -

Almost sure convergence of weighted sums

Abstract

Scopus Subject Areas

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