Amendments and Corrections: Bias Reduction of Maximum Likelihood Estimates

Biometrika ◽  
1995 ◽  
Vol 82 (3) ◽  
pp. 667
Author(s):  
David Firth
Keyword(s):  
Maximum Likelihood ◽  
Bias Reduction ◽  
Maximum Likelihood Estimates

scholarly journals Bias-Corrected Maximum Likelihood Estimators of the Parameters of the Unit-Weibull Distribution

2021 ◽  
Vol 50 (3) ◽  
pp. 41-53
Author(s):  
Andre Menezes ◽  
Josmar Mazucheli ◽  
F. Alqallaf ◽  
M. E. Ghitany
Keyword(s):  
Maximum Likelihood ◽  
Weibull Distribution ◽  
Parametric Bootstrap ◽  
Real Data ◽  
Bias Reduction ◽  
Maximum Likelihood Estimates ◽  
Data Sets ◽  
Analytical Methodology ◽  
Finite Samples ◽  
Modeling Data

It is well known that the maximum likelihood estimates (MLEs) have appealing statistical properties. Under fairly mild conditions their asymptotic distribution is normal, and no other estimator has a smaller asymptotic variance.However, in finite samples the maximum likelihood estimates are often biased estimates and the bias disappears as the sample size grows.Mazucheli, Menezes, and Ghitany (2018b) introduced a two-parameter unit-Weibull distribution which is useful for modeling data on the unit interval, however its MLEs are biased in finite samples.In this paper, we adopt three approaches for bias reduction of the MLEs of the parameters of unit-Weibull distribution.The first approach is the analytical methodology suggested by Cox and Snell (1968), the second is based on parametric bootstrap resampling method, and the third is the preventive approach introduced by Firth (1993).The results from Monte Carlo simulations revealed that the biases of the estimates should not be ignored and the bias reduction approaches are equally efficient. However, the first approach is easier to implement.Finally, applications to two real data sets are presented for illustrative purposes.

scholarly journals Median bias reduction of maximum likelihood estimates

Biometrika ◽  
2017 ◽  
Vol 104 (4) ◽  
pp. 923-938 ◽  
Author(s):  
E C Kenne Pagui ◽  
A Salvan ◽  
N Sartori
Keyword(s):  
Maximum Likelihood ◽  
Bias Reduction ◽  
Maximum Likelihood Estimates

scholarly journals Solutions to problems of nonexistence of parameter estimates and sparse data bias in Poisson regression

2021 ◽  
pp. 096228022110654
Author(s):  
Ashwini Joshi ◽  
Angelika Geroldinger ◽  
Lena Jiricka ◽  
Pralay Senchaudhuri ◽  
Christopher Corcoran ◽  
...  
Keyword(s):  
Maximum Likelihood ◽  
Poisson Regression ◽  
Sparse Data ◽  
Bias Reduction ◽  
Maximum Likelihood Estimates ◽  
Regression Coefficients ◽  
Bayesian Estimator ◽  
Parameter Estimates ◽  
Small Data ◽  
Conditional Poisson

Poisson regression can be challenging with sparse data, in particular with certain data constellations where maximum likelihood estimates of regression coefficients do not exist. This paper provides a comprehensive evaluation of methods that give finite regression coefficients when maximum likelihood estimates do not exist, including Firth’s general approach to bias reduction, exact conditional Poisson regression, and a Bayesian estimator using weakly informative priors that can be obtained via data augmentation. Furthermore, we include in our evaluation a new proposal for a modification of Firth’s approach, improving its performance for predictions without compromising its attractive bias-correcting properties for regression coefficients. We illustrate the issue of the nonexistence of maximum likelihood estimates with a dataset arising from the recent outbreak of COVID-19 and an example from implant dentistry. All methods are evaluated in a comprehensive simulation study under a variety of realistic scenarios, evaluating their performance for prediction and estimation. To conclude, while exact conditional Poisson regression may be confined to small data sets only, both the modification of Firth’s approach and the Bayesian estimator are universally applicable solutions with attractive properties for prediction and estimation. While the Bayesian method needs specification of prior variances for the regression coefficients, the modified Firth approach does not require any user input.

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