scholarly journals Bounds for the normal approximation of the maximum likelihood estimator fromm-dependent random variables

2017 ◽  
Vol 129 ◽  
pp. 171-181
Author(s):  
Andreas Anastasiou
Keyword(s):  
Maximum Likelihood ◽  
Maximum Likelihood Estimator ◽  
Normal Approximation ◽  
Random Variables ◽  
Likelihood Estimator ◽  
Dependent Random Variables

Asymptotic Bias in Simulated Maximum Likelihood Estimation of Discrete Choice Models

1995 ◽  
Vol 11 (3) ◽  
pp. 437-483 ◽  
Author(s):  
Lung-Fei Lee
Keyword(s):  
Asymptotic Expansion ◽  
Maximum Likelihood ◽  
Sample Size ◽  
Maximum Likelihood Estimator ◽  
Discrete Choice ◽  
Random Variables ◽  
Discrete Choice Models ◽  
Asymptotic Bias ◽  
Likelihood Estimator ◽  
Simulated Maximum Likelihood

In this article, we investigate a bias in an asymptotic expansion of the simulated maximum likelihood estimator introduced by Lerman and Manski (pp. 305–319 in C. Manski and D. McFadden (eds.), Structural Analysis of Discrete Data with Econometric Applications, Cambridge: MIT Press, 1981) for the estimation of discrete choice models. This bias occurs due to the nonlinearity of the derivatives of the log likelihood function and the statistically independent simulation errors of the choice probabilities across observations. This bias can be the dominating bias in an asymptotic expansion of the simulated maximum likelihood estimator when the number of simulated random variables per observation does not increase at least as fast as the sample size. The properly normalized simulated maximum likelihood estimator even has an asymptotic bias in its limiting distribution if the number of simulated random variables increases only as fast as the square root of the sample size. A bias-adjustment is introduced that can reduce the bias. Some Monte Carlo experiments have demonstrated the usefulness of the bias-adjustment procedure.

scholarly journals Estimation of P{X < Y} for gamma exponential model

2014 ◽  
Vol 24 (2) ◽  
pp. 283-291 ◽  
Author(s):  
Milan Jovanovic ◽  
Vesna Rajic
Keyword(s):  
Maximum Likelihood ◽  
Maximum Likelihood Estimator ◽  
Exponential Distribution ◽  
Asymptotic Distribution ◽  
Simulation Study ◽  
Random Variables ◽  
Exponential Model ◽  
Independent Random Variables ◽  
Likelihood Estimator

In this paper, we estimate probability P{X < Y} when X and Y are two independent random variables from gamma and exponential distribution, respectively. We obtain maximum likelihood estimator and its asymptotic distribution. We perform some simulation study.

The Comparison Between the Bayes Estimator and the Maximum Likelihood Estimator of the Reliability Function for Negative Exponential Distribution

2018 ◽  
pp. 439
Author(s):  
Hazim Mansour Gorgees ◽  
Bushra Abdualrasool Ali ◽  
Raghad Ibrahim Kathum
Keyword(s):  
Maximum Likelihood ◽  
Maximum Likelihood Estimator ◽  
Exponential Distribution ◽  
Reliability Function ◽  
Bayes Estimator ◽  
Likelihood Estimator ◽  
Monte Carlo Simulation Technique ◽  
Negative Exponential Distribution ◽  
Negative Exponential ◽  
Better Than

     In this paper, the maximum likelihood estimator and the Bayes estimator of the reliability function for negative exponential distribution has been derived, then a Monte –Carlo simulation technique was employed to compare the performance of such estimators. The integral mean square error (IMSE) was used as a criterion for this comparison. The simulation results displayed that the Bayes estimator performed better than the maximum likelihood estimator for different samples sizes.

scholarly journals Transforming variables to central normality

2021 ◽  
Author(s):  
Jakob Raymaekers ◽  
Peter J. Rousseeuw
Keyword(s):  
Maximum Likelihood ◽  
Maximum Likelihood Estimator ◽  
Simulation Study ◽  
Real Data ◽  
Data Sets ◽  
Transformation Parameter ◽  
Likelihood Estimator ◽  
Extensive Simulation ◽  
Highly Sensitive

AbstractMany real data sets contain numerical features (variables) whose distribution is far from normal (Gaussian). Instead, their distribution is often skewed. In order to handle such data it is customary to preprocess the variables to make them more normal. The Box–Cox and Yeo–Johnson transformations are well-known tools for this. However, the standard maximum likelihood estimator of their transformation parameter is highly sensitive to outliers, and will often try to move outliers inward at the expense of the normality of the central part of the data. We propose a modification of these transformations as well as an estimator of the transformation parameter that is robust to outliers, so the transformed data can be approximately normal in the center and a few outliers may deviate from it. It compares favorably to existing techniques in an extensive simulation study and on real data.

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