The functional CLT for linear processes generated by mixing random variables with infinite variance

2008 ◽  
Vol 78 (14) ◽  
pp. 2095-2101 ◽  
Author(s):  
H.J. Moon
Keyword(s):  
Random Variables ◽  
Infinite Variance ◽  
Linear Processes ◽  
Functional Clt ◽  
Mixing Random Variables

scholarly journals Central limit theorem for linear processes generated by IID random variables under the sub-linear expectation

2021 ◽  
Vol 36 (2) ◽  
pp. 243-255
Author(s):  
Wei Liu ◽  
Yong Zhang
Keyword(s):  
Central Limit Theorem ◽  
Limit Theorem ◽  
Central Limit ◽  
Invariance Principle ◽  
Random Variables ◽  
Probability Measures ◽  
Linear Processes ◽  
The Central Limit Theorem

AbstractIn this paper, we investigate the central limit theorem and the invariance principle for linear processes generated by a new notion of independently and identically distributed (IID) random variables for sub-linear expectations initiated by Peng [19]. It turns out that these theorems are natural and fairly neat extensions of the classical Kolmogorov’s central limit theorem and invariance principle to the case where probability measures are no longer additive.

scholarly journals A Shortcut to LAD Estimator Asymptotics

1991 ◽  
Vol 7 (4) ◽  
pp. 450-463 ◽  
Author(s):  
P.C.B. Phillips
Keyword(s):  
Asymptotic Expansion ◽  
Regression Model ◽  
Taylor Series ◽  
Asymptotic Theory ◽  
Random Variables ◽  
Generalized Functions ◽  
Infinite Variance ◽  
Series Expansions ◽  
Linear Functionals ◽  
Taylor Series Expansions

Using generalized functions of random variables and generalized Taylor series expansions, we provide quick demonstrations of the asymptotic theory for the LAD estimator in a regression model setting. The approach is justified by the smoothing that is delivered in the limit by the asymptotics, whereby the generalized functions are forced to appear as linear functionals wherein they become real valued. Models with fixed and random regressors, and autoregressions with infinite variance errors are studied. Some new analytic results are obtained including an asymptotic expansion of the distribution of the LAD estimator.

scholarly journals On the law of the iterated logarithm in the infinite variance case

1980 ◽  
Vol 30 (1) ◽  
pp. 5-14 ◽  
Author(s):  
R. A. Maller
Keyword(s):  
Sufficient Conditions ◽  
Random Variables ◽  
Necessary And Sufficient Conditions ◽  
Infinite Variance ◽  
Iterated Logarithm ◽  
The Law ◽  
Necessary And Sufficient ◽  
Independent And Identically Distributed

AbstractThe main purpose of the paper is to give necessary and sufficient conditions for the almost sure boundedness of (Sn – αn)/B(n), where Sn = X1 + X2 + … + XmXi being independent and identically distributed random variables, and αnand B(n) being centering and norming constants. The conditions take the form of the convergence or divergence of a series of a geometric subsequence of the sequence P(Sn − αn > a B(n)), where a is a constant. The theorem is distinguished from previous similar results by the comparative weakness of the subsidiary conditions and the simplicity of the calculations. As an application, a law of the iterated logarithm general enough to include a result of Feller is derived.

A note on the Bahadur representation of sample quantiles for α-mixing random variables

2011 ◽  
Vol 165 (3-4) ◽  
pp. 579-596 ◽  
Author(s):  
Guo-dong Xing ◽  
Shan-chao Yang ◽  
Yan Liu ◽  
Ke-ming Yu
Keyword(s):  
Random Variables ◽  
Bahadur Representation ◽  
Sample Quantiles ◽  
Mixing Random Variables

Mixing

2021 ◽  
pp. 290-312
Author(s):  
James Davidson
Keyword(s):  
Sufficient Conditions ◽  
Random Variables ◽  
Linear Processes ◽  
Mixing Sequences

The concepts of strong and uniform mixing are developed in the context of sequences of random variables. A set of important inequalities limiting the dependence of mixing sequences is proved. The case of linear processes is examined in depth including some well‐known counterexamples. Sufficient conditions are derived for strong and uniform mixing of linear processes.

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