On the Bias of the Maximum Likelihood Estimator for the Two-Parameter Lomax Distribution

Giles, David E. A.; Feng, Hui; Godwin, Ryan T.

doi:10.1080/03610926.2011.600506

Cited by 59 publications

(40 citation statements)

References 29 publications

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“…This bias can only be corrected by the indirect inference estimator with H samples of size n. In this case, even the MLE has a clear bias, since the asymptotic consistency of MLE does not demonstrate at such small sample. This is a well known issue, and in the case of the Lomax distribution, Giles et al (2013) derive the analytical expression of the finite sample bias. However, analytical correction for finite sample bias of the MLE is by far not available for all income distribution whereas simulation based bias correction methods can always be applied.…”

Section: Application To Robust Estimation Of Income Distributionmentioning

confidence: 99%

Simulation-Based Bias Correction Methods for Complex Models

Guerrier

Dupuis-Lozeron

Victoria‐Feser

2018

Journal of the American Statistical Association

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Along the ever increasing data size and model complexity, an important challenge frequently encountered in constructing new estimators or in implementing a classical one such as the maximum likelihood estimator, is the computational aspect of the estimation procedure. To carry out estimation, approximate methods such as pseudo-likelihood functions or approximated estimating equations are increasingly used in practice as these methods are typically easier to implement numerically although they can lead to inconsistent and/or biased estimators.In this context, we extend and provide refinements on the known bias 1 correction properties of two simulation based methods, respectively indirect inference and bootstrap, each with two alternatives. These results allow one to build a framework defining simulation based estimators that can be implemented for complex models. Indeed, based on a biased or even inconsistent estimator, several simulation based methods can be used to define new estimators that are both consistent and with reduced finite sample bias. This framework includes the classical method of indirect inference for bias correction without requiring specification of an auxiliary model. We demonstrate the equivalence between one version of the indirect inference and the iterative bootstrap, both correct sample biases up to the order n −3 .The iterative method can be thought of as a computationally efficient algorithm to solve the optimization problem of the indirect inference.Our results provide different tools to correct the asymptotic as well as finite sample biases of estimators and give insight on which method should be applied for the problem at hand. The usefulness of the proposed approach is illustrated with the estimation of robust income distributions and generalized linear latent variable models.

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Section: Application To Robust Estimation Of Income Distributionmentioning

confidence: 99%

Simulation-Based Bias Correction Methods for Complex Models

Guerrier

Dupuis-Lozeron

Victoria‐Feser

2018

Journal of the American Statistical Association

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“…However, no matter which method was used to find the maximum likelihood estimates of the parameters, these estimates were biased. Alternatively, we could have followed the work of Giles et al (2013). In that paper, the authors carried out an exploration of the bias of the maximum likelihood estimators of the Lomax distribution parameters.…”

Section: Discussionmentioning

confidence: 99%

A Note on Parameter Estimation in the Composite Weibull–Pareto Distribution

Calderín–Ojeda

2018

Risks

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Composite models have received much attention in the recent actuarial literature to describe heavy-tailed insurance loss data. One of the models that presents a good performance to describe this kind of data is the composite Weibull-Pareto (CWL) distribution. On this note, this distribution is revisited to carry out estimation of parameters via mle and mle2 optimization functions in R. The results are compared with those obtained in a previous paper by using the nlm function, in terms of analytical and graphical methods of model selection. In addition, the consistency of the parameter estimation is examined via a simulation study.

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“…While there is a substantial literature extending these works, of particular import to this article is the contribution of Cordeiro and Klein (1994), where analytical determination of the O(n −1 ) bias expression is somewhat simplified. Applications of Cordeiro and Klein's procedure for finding the O(n −1 ) bias expression may be found in Giles (2012), Giles et al (2013), Schwartz et al (2013), Xiao and Giles (2014), and Schwartz and Giles (forthcoming).…”

Section: Introductionmentioning

confidence: 97%

Bias reduction for the maximum likelihood estimator of the doubly-truncated Poisson distribution

Godwin¹

2016

Communications in Statistics - Theory and Methods

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We derive an analytic expression for the bias of the maximum likelihood estimator of the parameter in a doubly-truncated Poisson distribution, which proves highly effective as a means of bias correction. For smaller sample sizes, our method outperforms the alternative of bias correction via the parametric bootstrap. Bias is of little concern in the positive Poisson distribution, the most common form of truncation in the applied literature. Bias appears to be the most severe in the doubly-truncated Poisson distribution, when the mean of the distribution is close to the right (upper) truncation.

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On the Bias of the Maximum Likelihood Estimator for the Two-Parameter Lomax Distribution

Cited by 59 publications

References 29 publications

Simulation-Based Bias Correction Methods for Complex Models

Simulation-Based Bias Correction Methods for Complex Models

A Note on Parameter Estimation in the Composite Weibull–Pareto Distribution

Bias reduction for the maximum likelihood estimator of the doubly-truncated Poisson distribution

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