On Estimates of the Rate of Convergence in the Central Limit Theorem for Homogeneous Markov Chains

Sirazhdinov, S. Kh.; Formanov, Sh. K.

doi:10.1137/1128022

Cited by 5 publications

(2 citation statements)

References 8 publications

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“…The rate of convergence in ( 10) is uniform in a neighborhood of Π and also Π C → Π C almost surely (a.s.) as T → ∞ (Lifshits, 1979;Sirazhdinov and Formanov, 1984).…”

Section: Asymptotic Properties Of the Mdpdementioning

confidence: 97%

Robust Parametric Inference for Finite Markov Chains

Ghosh¹

2020

Preprint

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We consider the problem of statistical inference in a parametric finite Markov chain model and develop a robust estimator of the parameters defining the transition probabilities via the minimization of a suitable (empirical) version of the popular density power divergence. Based on a long sequence of observations from the underlying first-order stationary Markov chain, we have defined the minimum density power divergence estimator (MDPDE) of the underlying parameter and rigorously derive its asymptotic and robustness properties under appropriate conditions. The performance of our proposed MDPDEs are illustrated theoretically as well as empirically for several common examples of finite Markov chain models. The application of the MDPDE in robust testing of statistical hypotheses is discussed along with the (parametric) comparison of two Markov chain sequences. Finally, several directions for extending the proposed approach of MDPDE and related inference are also briefly discussed for some useful extended set-ups like multiple sequences of Markov chains, higher order Markov chains and non-stationary Markov chains with time-dependent transition probabilities.

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“…The rate of convergence in ( 10) is uniform in a neighborhood of Π and also Π C → Π C almost surely (a.s.) as T → ∞ (Lifshits, 1979;Sirazhdinov and Formanov, 1984).…”

Section: Asymptotic Properties Of the Mdpdementioning

confidence: 97%

Robust Parametric Inference for Finite Markov Chains

Ghosh¹

2020

Preprint

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“…This result was generalized by CUDYNAS [17]. Further papers in the matter are due to LANDERS and R000E [22], BOLTITAUSEN [2], GORDrN and LLFsmTs [16], SlxAznDncov and FoRIANov [29], and BRADLEY [4]. All in all, most of these articles use conditions which imply that the random variables are in some sense "asymptotically independent".…”

Section: Ze4(yf)mentioning

confidence: 99%

The Conditional Lindeberg–Trotter Operator in the Resolution of Limit Theorems with Rates for Dependent Random Variables. Applications to Markovian Processes

Butzer¹,

Kirschfink²

1988

Z. Anal. Anwend.

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Compound Poisson approximations for sums of Markov dependent random variables

Čekanavičius,

Liaudanskaitė

2024

Lith Math J

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On Estimates of the Rate of Convergence in the Central Limit Theorem for Homogeneous Markov Chains

Cited by 5 publications

References 8 publications

Robust Parametric Inference for Finite Markov Chains

Robust Parametric Inference for Finite Markov Chains

The Conditional Lindeberg–Trotter Operator in the Resolution of Limit Theorems with Rates for Dependent Random Variables. Applications to Markovian Processes

Compound Poisson approximations for sums of Markov dependent random variables

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