scholarly journals ON THE FIRST–ORDER EFFICIENCY AND ASYMPTOTIC NORMALITY OF MAXIMUM LIKELIHOOD ESTIMATORS OBTAINED FROM DEPENDENT OBSERVATIONS

1986 ◽  
Vol 40 (3) ◽  
pp. 169-188 ◽  
Author(s):  
R.D.H. Heijmans ◽  
J.R. Magnus
Keyword(s):  
Maximum Likelihood ◽  
Asymptotic Normality ◽  
Maximum Likelihood Estimators ◽  
First Order ◽  
Dependent Observations

Asymptotic Normmality of Maximum Likelihood Estimators Obtained from Normally Distributed but Dependent Observations

1986 ◽  
Vol 2 (3) ◽  
pp. 374-412 ◽  
Author(s):  
Risto D. H. Heijmans ◽  
Jan R. Magnus
Keyword(s):  
Maximum Likelihood ◽  
Asymptotic Normality ◽  
Maximum Likelihood Estimators ◽  
First Order ◽  
Dependent Observations ◽  
Identical Distribution ◽  
Special Case ◽  
Normally Distributed

In this article we aim to establish intuitively appealing and verifiable conditions for the first-order efficiency and asymptotic normality of ML estimators in a multi-parameter framework, assuming joint normality but neither the independence nor the identical distribution of the observations. We present five theorems (and a large number of lemmas and propositions), each being a special case of its predecessor.

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.

Sign in / Sign up

Export Citation Format

Share Document