A central limit theorem for nonhomogeneous semi-Markov random evolutions

1989 ◽  
Vol 41 (8) ◽  
pp. 912-918
Author(s):  
V. S. Korolyuk ◽  
A. V. Svishchuk
Keyword(s):  
Central Limit Theorem ◽  
Limit Theorem ◽  
Central Limit ◽  
Markov Random ◽  
Random Evolutions

scholarly journals Central limit theorem for semi-markov random evolutions

1990 ◽  
Vol 19 (1) ◽  
pp. 83-88 ◽  
Author(s):  
V.S. Koroljuk
Keyword(s):  
Central Limit Theorem ◽  
Limit Theorem ◽  
Central Limit ◽  
Markov Random ◽  
Random Evolutions

Central limit theorem for Semi-Markov random evolutions

1987 ◽  
Vol 38 (3) ◽  
pp. 286-289
Author(s):  
V. S. Korolyuk ◽  
A. V. Svishchuk
Keyword(s):  
Central Limit Theorem ◽  
Limit Theorem ◽  
Central Limit ◽  
Markov Random ◽  
Random Evolutions

Central limit theorem in the phase extension scheme for semi-Markov random evolutions

1988 ◽  
Vol 39 (3) ◽  
pp. 243-248 ◽  
Author(s):  
V. S. Korolyuk ◽  
A. V. Svishchuk ◽  
V. V. Korolyuk
Keyword(s):  
Central Limit Theorem ◽  
Limit Theorem ◽  
Central Limit ◽  
Markov Random ◽  
Phase Extension ◽  
Random Evolutions

A central limit theorem for conditionally centred random fields with an application to Markov fields

1998 ◽  
Vol 35 (03) ◽  
pp. 608-621
Author(s):  
Francis Comets ◽  
Martin Janžura
Keyword(s):  
Central Limit Theorem ◽  
Limit Theorem ◽  
Central Limit ◽  
Random Fields ◽  
Markov Random Fields ◽  
Moment Condition ◽  
Markov Random ◽  
Pseudo Likelihood ◽  
Strict Positivity ◽  
Markov Fields

We prove a central limit theorem for conditionally centred random fields, under a moment condition and strict positivity of the empirical variance per observation. We use a random normalization, which fits non-stationary situations. The theorem applies directly to Markov random fields, including the cases of phase transition and lack of stationarity. One consequence is the asymptotic normality of the maximum pseudo-likelihood estimator for Markov fields in complete generality.

scholarly journals A Self-Normalized Central Limit Theorem for Markov Random Walks

2012 ◽  
Vol 44 (02) ◽  
pp. 452-478
Author(s):  
Cheng-Der Fuh ◽  
Tian-Xiao Pang
Keyword(s):  
Markov Chain ◽  
Random Walk ◽  
Central Limit Theorem ◽  
Limit Theorem ◽  
Random Walks ◽  
State Space ◽  
Central Limit ◽  
Infinite Variance ◽  
Markov Random ◽  
Markov Random Walk

Motivated by the study of the asymptotic normality of the least-squares estimator in the (autoregressive) AR(1) model under possibly infinite variance, in this paper we investigate a self-normalized central limit theorem for Markov random walks. That is, let {X n , n ≥ 0} be a Markov chain on a general state space X with transition probability P and invariant measure π. Suppose that an additive component S n takes values on the real line , and is adjoined to the chain such that {S n , n ≥ 1} is a Markov random walk. Assume that S n = ∑ k=1 n ξ k , and that {ξ n , n ≥ 1} is a nondegenerate and stationary sequence under π that belongs to the domain of attraction of the normal law with zero mean and possibly infinite variance. By making use of an asymptotic variance formula of S n / √n, we prove a self-normalized central limit theorem for S n under some regularity conditions. An essential idea in our proof is to bound the covariance of the Markov random walk via a sequence of weight functions, which plays a crucial role in determining the moment condition and dependence structure of the Markov random walk. As illustrations, we apply our results to the finite-state Markov chain, the AR(1) model, and the linear state space model.

A central limit theorem for conditionally centred random fields with an application to Markov fields

1998 ◽  
Vol 35 (3) ◽  
pp. 608-621 ◽  
Author(s):  
Francis Comets ◽  
Martin Janžura
Keyword(s):  
Central Limit Theorem ◽  
Limit Theorem ◽  
Central Limit ◽  
Random Fields ◽  
Markov Random Fields ◽  
Moment Condition ◽  
Markov Random ◽  
Pseudo Likelihood ◽  
Strict Positivity ◽  
Markov Fields

We prove a central limit theorem for conditionally centred random fields, under a moment condition and strict positivity of the empirical variance per observation. We use a random normalization, which fits non-stationary situations. The theorem applies directly to Markov random fields, including the cases of phase transition and lack of stationarity. One consequence is the asymptotic normality of the maximum pseudo-likelihood estimator for Markov fields in complete generality.

scholarly journals A Self-Normalized Central Limit Theorem for Markov Random Walks

2012 ◽  
Vol 44 (2) ◽  
pp. 452-478 ◽  
Author(s):  
Cheng-Der Fuh ◽  
Tian-Xiao Pang
Keyword(s):  
Markov Chain ◽  
Random Walk ◽  
Central Limit Theorem ◽  
Limit Theorem ◽  
Random Walks ◽  
State Space ◽  
Central Limit ◽  
Infinite Variance ◽  
Markov Random ◽  
Markov Random Walk

Motivated by the study of the asymptotic normality of the least-squares estimator in the (autoregressive) AR(1) model under possibly infinite variance, in this paper we investigate a self-normalized central limit theorem for Markov random walks. That is, let {Xn, n ≥ 0} be a Markov chain on a general state space X with transition probability P and invariant measure π. Suppose that an additive component Sn takes values on the real line , and is adjoined to the chain such that {Sn, n ≥ 1} is a Markov random walk. Assume that Sn = ∑k=1nξk, and that {ξn, n ≥ 1} is a nondegenerate and stationary sequence under π that belongs to the domain of attraction of the normal law with zero mean and possibly infinite variance. By making use of an asymptotic variance formula of Sn / √n, we prove a self-normalized central limit theorem for Sn under some regularity conditions. An essential idea in our proof is to bound the covariance of the Markov random walk via a sequence of weight functions, which plays a crucial role in determining the moment condition and dependence structure of the Markov random walk. As illustrations, we apply our results to the finite-state Markov chain, the AR(1) model, and the linear state space model.

Applets Demonstrating the Central Limit Theorem and Statistical Power

2007 ◽  
Author(s):  
Amanda Saw ◽  
Dale E. Berger ◽  
Giovanni Sosa
Keyword(s):  
Central Limit Theorem ◽  
Limit Theorem ◽  
Central Limit ◽  
Statistical Power ◽  
The Central Limit Theorem

Central limit theorem for weakly dependent random fields with values in $l_p$ ($1 \lep \le2$) and $c_0$ spaces

2020 ◽  
Vol 2020 (1) ◽  
pp. 116-122
Author(s):  
D.S. Ruzieva ◽  
O.Sh. Sharipov
Keyword(s):  
Central Limit Theorem ◽  
Limit Theorem ◽  
Central Limit ◽  
Random Fields ◽  
Weakly Dependent
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