Asymptotic normality of maximum likelihood estimators for multiparameter Markov chains

1999 ◽  
Vol 20 (2) ◽  
pp. 309-312
Author(s):  
M. H. Al-Towaiq
Keyword(s):  
Maximum Likelihood ◽  
Markov Chains ◽  
Asymptotic Normality ◽  
Maximum Likelihood Estimators

New Ways to Prove Central Limit Theorems

1985 ◽  
Vol 1 (3) ◽  
pp. 295-313 ◽  
Author(s):  
David Pollard
Keyword(s):  
Maximum Likelihood ◽  
Asymptotic Normality ◽  
Central Limit ◽  
Limit Theorems ◽  
Maximum Likelihood Estimators ◽  
Empirical Processes ◽  
Central Limit Theorems ◽  
Criterion Function ◽  
Nonstandard Conditions

This paper describes some techniques for proving asymptotic normality of statistics defined by maximization of random criterion function. The techniques are based on a combination of recent results from the theory of empirical processes and a method of Huber for the study of maximum likelihood estimators under nonstandard conditions.

Asymptotic Normality of some Estimators

1981 ◽  
Vol 30 (1-2) ◽  
pp. 13-22
Author(s):  
Adnan M. Awad
Keyword(s):  
Central Limit Theorem ◽  
Maximum Likelihood ◽  
Limit Theorem ◽  
Asymptotic Normality ◽  
Central Limit ◽  
Continuous Mapping ◽  
Maximum Likelihood Estimators ◽  
Posterior Distributions ◽  
Martingale Central Limit Theorem ◽  
Log Likelihood

This paper uses martingale central limit theorem and continuous mapping theorem to establish asymptotic normality of log-likelihood ratio process, maximum likelihood estimators and the posterior distributions. Illustrative examples are given.

scholarly journals Maximum Likelihood Estimation in the Fractional Vasicek Model

2017 ◽  
Vol 56 (1) ◽  
pp. 77-87 ◽  
Author(s):  
Stanislav Lohvinenko ◽  
Kostiantyn Ralchenko
Keyword(s):  
Brownian Motion ◽  
Maximum Likelihood ◽  
Maximum Likelihood Estimation ◽  
Asymptotic Normality ◽  
Maximum Likelihood Estimators ◽  
Likelihood Estimation ◽  
Hurst Parameter ◽  
Unknown Parameters ◽  
Vasicek Model ◽  
Consistency And Asymptotic Normality

We consider the fractional Vasicek model of the form dXt = (α-βXt)dt +γdBHt , driven by fractional Brownian motion BH with Hurst parameter H ∈ (1/2,1). We construct the maximum likelihood estimators for unknown parameters α and β, and prove their consistency and asymptotic normality.

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