A note on the existence and uniqueness of quasi-maximum likelihood estimators for mixed regressive, spatial autoregression models

2013 ◽  
Vol 83 (2) ◽  
pp. 568-572 ◽  
Author(s):  
Mengyuan Li ◽  
Dalei Yu ◽  
Peng Bai
Keyword(s):  
Maximum Likelihood ◽  
Existence And Uniqueness ◽  
Maximum Likelihood Estimators ◽  
Spatial Autoregression ◽  
Autoregression Models ◽  
Quasi Maximum Likelihood

scholarly journals On the Existence and Uniqueness of the Maximum Likelihood Estimators of Normal and Lognormal Population Parameters with Grouped Data

2009 ◽  
Vol 2009 ◽  
pp. 1-16 ◽  
Author(s):  
Jin Xia ◽  
Jie Mi ◽  
YanYan Zhou
Keyword(s):  
Maximum Likelihood ◽  
Lognormal Distribution ◽  
Existence And Uniqueness ◽  
Maximum Likelihood Estimators ◽  
Invariance Property ◽  
Type I ◽  
Grouped Data ◽  
Sample Data ◽  
Censored Sample ◽  
Two Parameters

Lognormal distribution has abundant applications in various fields. In literature, most inferences on the two parameters of the lognormal distribution are based on Type-I censored sample data. However, exact measurements are not always attainable especially when the observation is below or above the detection limits, and only the numbers of measurements falling into predetermined intervals can be recorded instead. This is the so-called grouped data. In this paper, we will show the existence and uniqueness of the maximum likelihood estimators of the two parameters of the underlying lognormal distribution with Type-I censored data and grouped data. The proof was first established under the case of normal distribution and extended to the lognormal distribution through invariance property. The results are applied to estimate the median and mean of the lognormal population.

Finite-Sample Theory and Bias Correction of Maximum Likelihood Estimators in the EGARCH Model

2018 ◽  
Vol 11 (1) ◽  
Author(s):  
Antonis Demos ◽  
Dimitra Kyriakopoulou
Keyword(s):  
Monte Carlo ◽  
Maximum Likelihood ◽  
Bias Correction ◽  
Maximum Likelihood Estimators ◽  
Finite Sample ◽  
Egarch Model ◽  
Quasi Maximum Likelihood ◽  
Measure Of Performance ◽  
Analytical Expressions ◽  
Better Than

AbstractWe derive the analytical expressions of bias approximations for maximum likelihood (ML) and quasi-maximum likelihood (QML) estimators of the EGARCH (1,1) parameters that enable us to correct after the bias of all estimators. The bias-correction mechanism is constructed under the specification of two methods that are analytically described. We also evaluate the residual bootstrapped estimator as a measure of performance. Monte Carlo simulations indicate that, for given sets of parameters values, the bias corrections work satisfactory for all parameters. The proposed full-step estimator performs better than the classical one and is also faster than the bootstrap. The results can be also used to formulate the approximate Edgeworth distribution of the estimators.

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