Laws of iterated logarithm for quasi-maximum likelihood estimator in generalized linear model

2008 ◽  
Vol 138 (3) ◽  
pp. 611-617 ◽  
Author(s):  
Zhihong Xiao ◽  
Luqin Liu
Keyword(s):  
Maximum Likelihood ◽  
Maximum Likelihood Estimator ◽  
Linear Model ◽  
Generalized Linear Model ◽  
Likelihood Estimator ◽  
Iterated Logarithm ◽  
Quasi Maximum Likelihood ◽  
Laws Of Iterated Logarithm

scholarly journals Improving the Efficiency of Robust Estimators for the Generalized Linear Model

Stats ◽  
2021 ◽  
Vol 4 (1) ◽  
pp. 88-107
Author(s):  
Alfio Marazzi
Keyword(s):  
Maximum Likelihood ◽  
Maximum Likelihood Estimator ◽  
Linear Model ◽  
Negative Binomial ◽  
Small Sample ◽  
Hospital Length Of Stay ◽  
Robust Estimator ◽  
Negative Binomial Regression Model ◽  
Likelihood Estimator ◽  
Density Power Divergence

The distance constrained maximum likelihood procedure (DCML) optimally combines a robust estimator with the maximum likelihood estimator with the purpose of improving its small sample efficiency while preserving a good robustness level. It has been published for the linear model and is now extended to the GLM. Monte Carlo experiments are used to explore the performance of this extension in the Poisson regression case. Several published robust candidates for the DCML are compared; the modified conditional maximum likelihood estimator starting with a very robust minimum density power divergence estimator is selected as the best candidate. It is shown empirically that the DCML remarkably improves its small sample efficiency without loss of robustness. An example using real hospital length of stay data fitted by the negative binomial regression model is discussed.

An Asymptotic Expansion in the GARCH(l, 1) Model

1997 ◽  
Vol 13 (4) ◽  
pp. 558-581 ◽  
Author(s):  
Oliver Linton
Keyword(s):  
Distribution Function ◽  
Asymptotic Expansion ◽  
Maximum Likelihood ◽  
Maximum Likelihood Estimator ◽  
Asymptotic Expansions ◽  
Bias Reduction ◽  
Likelihood Estimator ◽  
Quasi Maximum Likelihood

We develop order T−1 asymptotic expansions for the quasi-maximum likelihood estimator (QMLE) and a two-step approximate QMLE in the GARCH(l,l) model. We calculate the approximate mean and skewness and, hence, the Edgeworth-B distribution function. We suggest several methods of bias reduction based on these approximations.

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