Maximum Likelihood Estimators for ARMA and ARFIMA Models: A Monte Carlo Study

1998 ◽  
Author(s):  
Michael A. Hauser
Keyword(s):  
Monte Carlo ◽  
Maximum Likelihood ◽  
Maximum Likelihood Estimators ◽  
Monte Carlo Study ◽  
Arfima Models

scholarly journals No Need to Turn Bayesian in Multilevel Analysis with Few Clusters: How Frequentist Methods Provide Unbiased Estimates and Accurate Inference

2016 ◽  
Author(s):  
Martin Elff ◽  
Jan Paul Heisig ◽  
Merlin Schaeffer ◽  
Susumu Shikano
Keyword(s):  
Monte Carlo ◽  
Maximum Likelihood ◽  
Multilevel Analysis ◽  
Degrees Of Freedom ◽  
Multilevel Models ◽  
Maximum Likelihood Estimators ◽  
Monte Carlo Study ◽  
Bayesian Techniques ◽  
Upper Level ◽  
T Distribution

Comparative political science has long worried about the performance of multilevel models when the number of upper-level units is small. Exacerbating these concerns, an influential Monte Carlo study by Stegmueller (2013) suggests that frequentist methods yield biased estimates and severely anti-conservative inference with small upper-level samples. Stegmueller recommends Bayesian techniques, which he claims to be superior in terms of both bias and inferential accuracy. In this paper, we reassess and refute these results. First, we formally prove that frequentist maximum likelihood estimators of coefficients are unbiased. The apparent bias found by Stegmueller is simply a manifestation of Monte Carlo Error. Second, we show how inferential problems can be overcome by using restricted maximum likelihood estimators for variance parameters and a t-distribution with appropriate degrees of freedom for statistical inference. Thus, accurate multilevel analysis is possible without turning to Bayesian methods, even if the number of upper-level units is small.

scholarly journals Skewness of Maximum Likelihood Estimators in the Weibull Censored Data

Symmetry ◽  
2019 ◽  
Vol 11 (11) ◽  
pp. 1351 ◽  
Author(s):  
Tiago M. Magalhães ◽  
Diego I. Gallardo ◽  
Héctor W. Gómez
Keyword(s):  
Monte Carlo ◽  
Maximum Likelihood ◽  
Sample Size ◽  
Censored Data ◽  
Maximum Likelihood Estimators ◽  
Monte Carlo Study ◽  
Parameter Distribution ◽  
Regression Parameter ◽  
Skewness Coefficient ◽  
Matrix Formula

In this paper, we obtain a matrix formula of order n − 1 / 2 , where n is the sample size, for the skewness coefficient of the distribution of the maximum likelihood estimators in the Weibull censored data. The present result is a nice approach to verify if the assumption of the normality of the regression parameter distribution is satisfied. Also, the expression derived is simple, as one only has to define a few matrices. We conduct an extensive Monte Carlo study to illustrate the behavior of the skewness coefficient and we apply it in two real datasets.

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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