scholarly journals Statistical inference using maximum likelihood estimation and the generalized likelihood ratio when the true parameter is on the boundary of the parameter space

1992 ◽  
Vol 13 (4) ◽  
pp. 325-332 ◽  
Author(s):  
Ziding Feng ◽  
Charles E. McCulloch
Keyword(s):  
Maximum Likelihood ◽  
Maximum Likelihood Estimation ◽  
Statistical Inference ◽  
Likelihood Ratio ◽  
Parameter Space ◽  
Likelihood Estimation ◽  
True Parameter ◽  
Generalized Likelihood Ratio

Maximum-likelihood estimation in non-standard conditions

1971 ◽  
Vol 70 (3) ◽  
pp. 441-450 ◽  
Author(s):  
P. A. P. Moran
Keyword(s):  
Maximum Likelihood ◽  
Parameter Space ◽  
Null Hypothesis ◽  
Maximum Likelihood Estimators ◽  
Likelihood Estimation ◽  
Standard Theory ◽  
True Parameter ◽  
Open Set ◽  
Estimation Problems ◽  
Parameter Point

The origin of the present paper is the desire to study the asymptotic behaviour of certain tests of significance which can be based on maximum-likelihood estimators. The standard theory of such problems (e.g. Wald(4)) assumes, sometimes tacitly, that the parameter point corresponding to the null hypothesis lies inside an open set in the parameter space. Here we wish to study what happens when the true parameter point, in estimation problems, lies on the boundary of the parameter space.

Maximum Likelihood Estimation for MA(1) Processes with a Root on or near the Unit Circle

1996 ◽  
Vol 12 (1) ◽  
pp. 1-29 ◽  
Author(s):  
Richard A. Davis ◽  
William T.M. Dunsmuir
Keyword(s):  
Maximum Likelihood ◽  
Maximum Likelihood Estimation ◽  
Unit Circle ◽  
Asymptotic Distribution ◽  
Moving Average ◽  
Likelihood Estimation ◽  
Small Sample ◽  
Practical Significance ◽  
True Parameter ◽  
Small Sample Sizes

This paper considers maximum likelihood estimation for the moving average parameter θ in an MA(1) model when θ is equal to or close to 1. A derivation of the limit distribution of the estimate θLM, defined as the largest of the local maximizers of the likelihood, is given here for the first time. The theory presented covers, in a unified way, cases where the true parameter is strictly inside the unit circle as well as the noninvertible case where it is on the unit circle. The asymptotic distribution of the maximum likelihood estimator subMLE is also described and shown to differ, but only slightly, from that of θLM. Of practical significance is the fact that the asymptotic distribution for either estimate is surprisingly accurate even for small sample sizes and for values of the moving average parameter considerably far from the unit circle.

scholarly journals On estimation in multilevel models with block circular symmetric covariance structure

2012 ◽  
Vol 16 (1) ◽  
pp. 83-96
Author(s):  
Yuli Liang ◽  
Dietrich von Rosen ◽  
Tatjana von Rosen
Keyword(s):  
Maximum Likelihood ◽  
Maximum Likelihood Estimation ◽  
Parameter Space ◽  
Variance Components ◽  
Multilevel Model ◽  
Multilevel Models ◽  
Covariance Structure ◽  
Maximum Likelihood Estimators ◽  
Likelihood Estimation

In this article we consider a multilevel model with block circular symmetric covariance structure. Maximum likelihood estimation of the parameters of this model is discussed. We show that explicit maximum likelihood estimators of variance components exist under certain restrictions on the parameter space.

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