Statistical Inference Based on Pseudo-Maximum Likelihood Estimators in Elliptical Populations

1993 ◽  
Vol 88 (421) ◽  
pp. 135 ◽  
Author(s):  
Yutaka Kano ◽  
Maia Berkane ◽  
Peter M. Bentler
Keyword(s):  
Maximum Likelihood ◽  
Statistical Inference ◽  
Maximum Likelihood Estimators ◽  
Pseudo Maximum Likelihood

Noninvertibility and Pseudo-Maximum Likelihood Estimation of Misspecified ARMA Models

1991 ◽  
Vol 7 (4) ◽  
pp. 435-449 ◽  
Author(s):  
B.M. Pötscher
Keyword(s):  
Maximum Likelihood ◽  
Likelihood Function ◽  
Moving Average ◽  
Maximum Likelihood Estimators ◽  
Likelihood Estimation ◽  
Arma Models ◽  
Limiting Behavior ◽  
Pseudo Likelihood ◽  
Moving Average Model ◽  
Pseudo Maximum Likelihood

Recently Tanaka and Satchell [11] investigated the limiting properties of local maximizers of the Gaussian pseudo-likelihood function of a misspecified moving average model of order one in case the spectral density of the data process has a zero at frequency zero. We show that pseudo-maximum likelihood estimators in the narrower sense, that is, global maximizers of the Gaussian pseudo-likelihood function, may exhibit behavior drastically different from that of the local maximizers. Some general results on the limiting behavior of pseudo-maximum likelihood estimators in potentially misspecified ARMA models are also presented.

scholarly journals Principles of Statistical Inference: Likelihood and the Bayesian Paradigm

2010 ◽  
Vol 16 ◽  
pp. 1-18 ◽  
Author(s):  
Steve C. Wang
Keyword(s):  
Maximum Likelihood ◽  
Statistical Inference ◽  
Bayesian Approach ◽  
Subjective Probability ◽  
Prior Information ◽  
Maximum Likelihood Estimators ◽  
Likelihood Ratio Tests ◽  
Bayesian Paradigm ◽  
Point Estimators ◽  
The Bayesian Approach

We review two foundations of statistical inference, the theory of likelihood and the Bayesian paradigm. We begin by applying principles of likelihood to generate point estimators (maximum likelihood estimators) and hypothesis tests (likelihood ratio tests). We then describe the Bayesian approach, focusing on two controversial aspects: the use of prior information and subjective probability. We illustrate these analyses using simple examples.

STATISTICAL INFERENCE IN COINTEGRATED VECTOR AUTOREGRESSIVE MODELS WITH NONLINEAR TIME TRENDS IN COINTEGRATING RELATIONS

2001 ◽  
Vol 17 (2) ◽  
pp. 327-356 ◽  
Author(s):  
Pentti Saikkonen
Keyword(s):  
Maximum Likelihood ◽  
Statistical Inference ◽  
Likelihood Ratio ◽  
Lagrange Multiplier ◽  
Time Trends ◽  
Maximum Likelihood Estimators ◽  
Limiting Distributions ◽  
Vector Autoregressive Models ◽  
Vector Autoregressive ◽  
Short Run

This paper continues the work of Saikkonen (2001, Econometric Theory 17, 296–326) and develops an asymptotic theory of statistical inference in cointegrated vector autoregressive models with nonlinear time trends in cointegrating relations and general nonlinear parameter restrictions. Inference on parameters in cointegrating relations and short-run dynamics is studied separately. It is shown that Gaussian maximum likelihood estimators of parameters in cointegrating relations have mixed normal limiting distributions and that related Wald, Lagrange multiplier, and likelihood ratio tests for general nonlinear hypotheses have usual asymptotic chi-square distributions. These results are shown to hold even if parameters in the short-run dynamics are not identified. In that case suitable estimators of the information matrix have to be used to justify the application of Wald and Lagrange multiplier tests, whereas the likelihood ratio test is free of this difficulty. Similar results are also obtained when inference on parameters in the short-run dynamics is studied, although then Gaussian maximum likelihood estimators have usual normal limiting distributions. All results of the paper are proved without assuming existence of second partial derivatives of the likelihood function, and in some cases even differentiability with respect to nuisance parameters is not required.

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