A Central Limit Theorem for General Weighted Sums of LNQD Random Variables and Its Application

Ko, Mi-Hwa; Ryu, Dae-Hee; Kim, Taesung; Choi, Yong-Gab

doi:10.1216/rmjm/1181069330

Cited by 4 publications

(3 citation statements)

References 9 publications

Supporting

Mentioning

Contrasting

Order By: Relevance

“…where ν i , i = 1,…, p , is the i ‐th row of the matrix Q defined in and Γ is defined by

Γ = \lim_{p \to \infty} Σ_{i = 1}^{p} Σ_{j = 1}^{p} ν_{i} ν_{j}^{T} E (ϵ_{it} ϵ_{jt}) .

A9The limit,

\lim_{p \to \infty} p^{\frac{1 - δ}{2}} {normalΣ}_{f}^{- \frac{1}{2}} = H

, exists. Remark Since Q T Q = I r by construction, each element of Q has order of

O (\frac{1}{\sqrt{p}})

, thus Assumption A8 can be justified under various assumptions on { ϵ i t } such as martingale difference, mixing, associated or other weakly dependent processes. See, for example, Cocke (), McLeish (), Lahiri () and Ko et al (). From Proposition , we have

p^{\frac{1 - δ}{2}} Σ_{f}^{- \frac{1}{2}} = O (p^{\frac{1 - δ}{2}}) \cdot O_{p} (p^{- \frac{1 - δ}{2}}) = O_{p} (1) .

Thus

p^{\frac{1 - δ}{2}} {normalΣ}_{f}^{- \frac{1}{2}}

is bounded. Assumption A9 imposes an additional regularity on Σ f so that the asymptotic variance of

…”

Section: Resultsmentioning

confidence: 99%

See 1 more Smart Citation

Factor Modelling for High‐Dimensional Time Series: Inference and Model Selection

Chan

Yau

2016

Journal Time Series Analysis

View full text Add to dashboard Cite

Analysis of high‐dimensional time series data is of increasing interest among different fields. This article studies high‐dimensional time series from a dimension reduction perspective using factor modelling. Statistical inference is conducted using eigen‐analysis of a certain non‐negative definite matrix related to autocovariance matrices of the time series, which is applicable to fixed or increasing dimension. When the dimension goes to infinity, the rate of convergence and limiting distributions of estimated factors are established. Using the limiting distributions of estimated factors, a high‐dimensional final prediction error criterion is proposed to select the number of factors. Asymptotic properties of the criterion are illustrated by simulation studies and real applications.

show abstract

“…where ν i , i = 1,…, p , is the i ‐th row of the matrix Q defined in and Γ is defined by

Γ = \lim_{p \to \infty} Σ_{i = 1}^{p} Σ_{j = 1}^{p} ν_{i} ν_{j}^{T} E (ϵ_{it} ϵ_{jt}) .

A9The limit,

\lim_{p \to \infty} p^{\frac{1 - δ}{2}} {normalΣ}_{f}^{- \frac{1}{2}} = H

, exists. Remark Since Q T Q = I r by construction, each element of Q has order of

O (\frac{1}{\sqrt{p}})

p^{\frac{1 - δ}{2}} Σ_{f}^{- \frac{1}{2}} = O (p^{\frac{1 - δ}{2}}) \cdot O_{p} (p^{- \frac{1 - δ}{2}}) = O_{p} (1) .

Thus

p^{\frac{1 - δ}{2}} {normalΣ}_{f}^{- \frac{1}{2}}

is bounded. Assumption A9 imposes an additional regularity on Σ f so that the asymptotic variance of

…”

Section: Resultsmentioning

confidence: 99%

“…1 p p /, thus Assumption A8 can be justified under various assumptions on ¹" it º such as martingale difference, mixing, associated or other weakly dependent processes. See, for example, Cocke (1972), McLeish (1974), Lahiri (2003) and Ko et al (2007). 2.…”

Section: Asymptotic Normalitymentioning

confidence: 99%

Factor Modelling for High‐Dimensional Time Series: Inference and Model Selection

Chan

Yau

2016

Journal Time Series Analysis

View full text Add to dashboard Cite

show abstract

“…Joag-Dev and Proschan [7], Newman [12] and the references there in). Newmann [12] was first to establish a central limit theorem for LNQD random variables, Kim et al [9] derived a general central limit theorem for weighted sum of LNQD random variables. Firstly, we will recall the definitions of negatively associated, negative quadrant dependent and linearly negative quadrant dependent sequence.…”

Section: Introductionmentioning

confidence: 99%

Probability tail for linearly negative quadrant dependent random variables of partial sums and application to linear model

Kaddour¹,

Belguerna

Benaissa³

2022

J. Innov. Appl. Math. Comput. Sci

View full text Add to dashboard Cite

show abstract

Sobre la validez del supuesto de uniformidad en las tasas de plusvalía sectorial desde la teoría de las probabilidades

Gómez Julián

2022

View full text Add to dashboard Cite

El supuesto de uniformidad en las tasas de plusvalía sectorial se encuentra implícito en todo análisis marxista de la tasa media de ganancia que no tome explícitamente en consideración las diferencias en el grado de explotación de la fuerza de trabajo entre los diferentes sectores productivos. La validez de este supuesto, establecido por Adam Smith y elevado al grado de ley económica central en el marco teórico de Marx, ha sido cuestionada tanto desde posiciones marxistas como desde otras posiciones. Esta investigación analiza la consistencia lógica de tal supuesto, en términos de variedades no clásicas, de la ley de los grandes números tanto en su versión débil como fuerte, así como también examina, descriptiva e inferencialmente, el comportamiento empírico de las tasas de plusvalía sectorial en la economía estadounidense durante el periodo 1960-2020. Los resultados teóricos y aplicados arrojan evidencia a favor de la validez de este supuesto.

show abstract

A Central Limit Theorem for General Weighted Sums of LNQD Random Variables and Its Application

Cited by 4 publications

References 9 publications

Factor Modelling for High‐Dimensional Time Series: Inference and Model Selection

Factor Modelling for High‐Dimensional Time Series: Inference and Model Selection

Probability tail for linearly negative quadrant dependent random variables of partial sums and application to linear model

Sobre la validez del supuesto de uniformidad en las tasas de plusvalía sectorial desde la teoría de las probabilidades

Contact Info

Product

Resources

About