Asymptotic theory for imaging the attenuation factors Q P and Q S

2007 ◽  
pp. 334-353
Author(s):  
Alessandra Ribodetti ◽  
Jean Virieux
Keyword(s):  
Asymptotic Theory

The Asymptotic Theory of the Kakwani Class of Poverty Measures

2007 ◽  
Author(s):  
Gane Samb Lo ◽  
Serigne Touba Sall ◽  
Cheikh Tidiane Seck
Keyword(s):  
Asymptotic Theory ◽  
Poverty Measures

Standard Asymptotic Theory

2017 ◽  
Author(s):  
Russell Cheng
Keyword(s):  
Asymptotic Theory ◽  
Asymptotic Variance ◽  
Statistical Significance ◽  
Regularity Conditions ◽  
Parameter Estimates ◽  
Asymptotic Results ◽  
Ml Estimation ◽  
True Parameter ◽  
Log Likelihood ◽  
Ml Estimator

This book relies on maximum likelihood (ML) estimation of parameters. Asymptotic theory assumes regularity conditions hold when the ML estimator is consistent. Typically an additional third derivative condition is assumed to ensure that the ML estimator is also asymptotically normally distributed. Standard asymptotic results that then hold are summarized in this chapter; for example, the asymptotic variance of the ML estimator is then given by the Fisher information formula, and the log-likelihood ratio, the Wald and the score statistics for testing the statistical significance of parameter estimates are all asymptotically equivalent. Also, the useful profile log-likelihood then behaves exactly as a standard log-likelihood only in a parameter space of just one dimension. Further, the model can be reparametrized to make it locally orthogonal in the neighbourhood of the true parameter value. The large exponential family of models is briefly reviewed where a unified set of regular conditions can be obtained.

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