Bias-corrected maximum likelihood estimation for the beta distribution

Cordeiro, Gauss M.; Rocha, Enivaldo Carvalho da; Rocha, Jacira Guiro C. Da; Cribari‐Neto, Francisco

doi:10.1080/00949659708811820

Cited by 20 publications

(12 citation statements)

References 15 publications

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“…Also for this class of models, Cook et al (1986) show that the bias may be due to the explanatory variables position in the sample space. Cordeiro and McCullagh (1991) gave a general bias formulae in matrix notation for generalized linear models.Bias corrected versions of the MLEs of the parameters that index the beta distribution were obtained by Cordeiro et al (1997) and Cribari-Neto and Vasconcellos (2002). However, such results do not hold for models with regression structures.…”

mentioning

confidence: 98%

Improved estimators for a general class of beta regression models

Simas

Barreto‐Souza

Rocha

2010

Computational Statistics & Data Analysis

237

167

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In this paper we consider an extension of the beta regression model proposed by Ferrari and Cribari-Neto (2004). We extend their model in two different ways, first, we let the regression structure be nonlinear, second, we allow a regression structure for the precision parameter, moreover, this regression structure may also be nonlinear. Generally, the beta regression is useful to situations where the response is restricted to the standard unit interval and the regression structure involves regressors and unknown parameters. We derive general formulae for second-order biases of the maximum likelihood estimators and use them to define bias-corrected estimators. Our formulae generalizes the results obtained by Ospina et al. (2006), and are easily implemented by means of supplementary weighted linear regressions. We also compare these bias-corrected estimators with three different estimators which are also bias-free to the second-order, one analytical and the other two based on bootstrap methods. These estimators are compared by simulation. We present an empirical application

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mentioning

confidence: 98%

Improved estimators for a general class of beta regression models

Simas

Barreto‐Souza

Rocha

2010

Computational Statistics & Data Analysis

237

167

View full text Add to dashboard Cite

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“…Applying the corrective Cox-Snell methodology, many researchers have developed nearly unbiased estimators for the parameters of several probability distributions. Interested readers can refer to Cordeiro et al (1997), Cribari-Neto and Vasconcellos (2002), Saha and Paul (2005), Lemonte et al (2007), Giles and Feng (2009) Lagos-Álvarez et al (2011), Lemonte (2011), Giles (2012b), Giles (2012a), Schwartz et al (2013), , Teimouri and Nadarajah (2013), Xiao and Giles (2014), Zhang and Liu (2015), Teimouri and Nadarajah (2016), Reath (2016), , Schwartz and Giles (2016), , Mazucheli and Dey (2017) and references cited therein.…”

Section: Introductionmentioning

confidence: 99%

mle.tools: An R Package for Maximum Likelihood Bias Correction

Mazucheli¹,

Menezes²,

Nadarajah³

2017

The R Journal

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Recently, Mazucheli (2017) uploaded the package mle.tools to CRAN. It can be used for bias corrections of maximum likelihood estimates through the methodology proposed by Cox and Snell (1968). The main function of the package, coxsnell.bc(), computes the bias corrected maximum likelihood estimates. Although in general, the bias corrected estimators may be expected to have better sampling properties than the uncorrected estimators, analytical expressions from the formula proposed by Cox and Snell (1968) are either tedious or impossible to obtain. The purpose of this paper is twofolded: to introduce the mle.tools package, especially the coxsnell.bc() function; secondly, to compare, for thirty one continuous distributions, the bias estimates from the coxsnell.bc() function and the bias estimates from analytical expressions available in the literature. We also compare, for five distributions, the observed and expected Fisher information. Our numerical experiments show that the functions are efficient to estimate the biases by the Cox-Snell formula and for calculating the observed and expected Fisher information.

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“…A number of recent papers have successfully obtained analytic expressions for which are valid to O(n -1 ), based on the work of Cox and Snell (1968), and Cordeiro and Klein (1994). Some examples include: Cordeiro and McCullagh (1991), Cordeiro et al (1996), Cribari-Neto and Vasconcellos (2002), Cordeiro and Vasconcellos (1997), Silva et al (2008), Giles (2012), Giles et al (2013Giles et al ( , 2016, Schwartz et al (2013), Schwartz and Giles (2016), and Godwin (2016). A useful overview of this topic is provided by Cordeiro and Cribari-Neto (2014).…”

Section: Introductionmentioning

confidence: 99%

Analytic bias correction for maximum likelihood estimators when the bias function is non-constant

Godwin

Giles

2017

Communications in Statistics - Simulation and Computation

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Recently, many papers have obtained analytic expressions for the biases of various maximum likelihood estimators, despite their lack of closed-form solution. These bias expressions have provided an attractive alternative to the bootstrap. Unless the bias function is "flat," however, the expressions are being evaluated at the wrong point(s). We propose an "improved" analytic bias adjusted estimator, in which the bias expression is evaluated at a more appropriate point (at the bias adjusted estimator itself). Simulations illustrate that the improved analytic bias adjusted estimator can eliminate significantly more bias than the simple estimator which has been well established in the literature.

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Bias-corrected maximum likelihood estimation for the beta distribution

Cited by 20 publications

References 15 publications

Improved estimators for a general class of beta regression models

Improved estimators for a general class of beta regression models

mle.tools: An R Package for Maximum Likelihood Bias Correction

Analytic bias correction for maximum likelihood estimators when the bias function is non-constant

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