Bias Correction for a Generalized Log-Gamma Regression Model

Young, David H.; Bakir, Saad T.

doi:10.2307/1269773

Cited by 33 publications

(7 citation statements)

References 6 publications

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“…Over the last ten years, there have been many advances concerning bias calculation of nonlinear MLEs in regression models. We refer the reader to the papers by Cook, Tsai & Wei (1986), Young & Bakir (1987), Cordeiro & McCullagh (1991), Paula (1992), Cordeiro & Klein (1994), Paula & Cordeiro (1995) and Cordeiro & Vasconcellos (1997). Except for the paper by Young and Bakir, all other papers give matrix formulae which applied researchers can use to compute bias correction in special regression models.…”

Section: Introductionmentioning

confidence: 99%

Theory & Methods: Second‐order biases of the maximum likelihood estimates in von Mises regression models

Cordeiro

Vasconcellos

1999

Aus NZ J of Statistics

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This paper discusses issues related to the improvement of maximum likelihood estimates in von Mises regression models. It obtains general matrix expressions for the secondorder biases of maximum likelihood estimates of the mean parameters and concentration parameters. The formulae are simple to compute, and give the biases by means of weighted linear regressions. Simulation results are presented assessing the performance of corrected maximum likelihood estimates in these models.

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Section: Introductionmentioning

confidence: 99%

Theory & Methods: Second‐order biases of the maximum likelihood estimates in von Mises regression models

Cordeiro

Vasconcellos

1999

Aus NZ J of Statistics

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“…Furthermore, Fryer and Robertson (1972) compared moment estimates and multinomial MLEs and minimum x 2 estimates for bias to order n:' and mean-squared error to n:" for a variety of mixed distributions. Following the general formulae for the n:' biases developed by Cox and Snell (1968), Anderson and Richardson (1979) and McLachlan (1980) found the biases of the MLEs in logistic discrimination problems and Young and Bakir (1987) derived those in the generalized log-gamma regression model. An important recent paper by Cook et af.…”

Section: Introductionmentioning

confidence: 99%

Bias Correction in Generalized Linear Models

Cordeiro

McCullagh

1991

Journal of the Royal Statistical Society Series B: Statistical Methodology

176

140

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SUMMARY In this paper we derive general formulae for first‐order biases of maximum likelihood estimates of the linear parameters, linear predictors, the dispersion parameter and fitted values in generalized linear models. These formulae may be implemented in the GLIM program to compute bias‐corrected maximum likelihood estimates to order n−1, where n is the sample size, with minimal effort by means of a supplementary weighted regression. For linear logistic models it is shown that the asymptotic bias vector of trueβ̂ is almost collinear with β. The approximate formula βp/m+ for the bias of trueβ̂ in logistic models, where p = dim(β) and m+ = ∑ mi is the sum of the binomial indices, is derived and checked numerically.

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“…Consider the data analysed by Young and Bakir (1987) .. ,24, shows no evidence that the log gamma distribution is unsatisfactory. 'micro adiust $cal c2=\loq(z-p(3» : c3=-p(2)/(z-p(3» : c4=x2/(p(S)+x2) : cS:-p(4)*c4/(p(S)+x2) : of=-p(3)*c3-p(S)*cS 'offs of 'recycle 1 'fit c2+c3+c4+cS 'dis e 'ext \pe 'cil \lp=\pe(1)+\pe(2)*\log(z-\pe(3»+x2*\pe (4) …”

Section: Experiments With Speciments Of Stainless Steelmentioning

confidence: 99%