Diagnostics and Robust Estimation When Transforming the Regression Model and the Response.

Carroll, R. J.; Ruppert, David

doi:10.21236/ada177531

Cited by 4 publications

(3 citation statements)

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“…Further Bayesian considerations have also been outlined by Pericchi (1981) and Sweeting (1984). Some robust adaptations of the estimation procedures have been studied by Carroll (1980;, Bickel & Doksum (1981), Carroll and Ruppert (1985), Taylor (1983Taylor ( , 1985Taylor ( a, b, 1987 and Carroll & Ruppert (1987). The extension of the Box-Cox procedure to multivariate data has been proposed in Andrew etal.…”

Section: A=omentioning

confidence: 99%

The Box-Cox Transformation Technique: A Review

1992

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Section: A=omentioning

confidence: 99%

The Box-Cox Transformation Technique: A Review

1992

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“…In particular, we introduce maximum likelihood and residual maximum likelihood (REML) methods for estimating the transformation parameter under the linear mixed regression model following Gurka et al (2006). Alternative estimation approaches based on the minimization of distances (Cramér, 1928;Chakravarti et al, 1967) and on the minimization of the skewness (Carroll and Ruppert, 1987) are also discussed.…”

Section: Introductionmentioning

confidence: 99%

Data-Driven Transformations in Small Area Estimation

Rojas‐Perilla

Pannier

Schmid

et al. 2019

Journal of the Royal Statistical Society Series A: Statistics in Society

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Summary Small area models typically depend on the validity of model assumptions. For example, a commonly used version of the empirical best predictor relies on the Gaussian assumptions of the error terms of the linear mixed regression model: a feature rarely observed in applications with real data. The paper tackles the potential lack of validity of the model assumptions by using data‐driven scaled transformations as opposed to ad hoc chosen transformations. Different types of transformations are explored, the estimation of the transformation parameters is studied in detail under the linear mixed regression model and transformations are used in small area prediction of linear and non‐linear parameters. The use of scaled transformations is crucial as it enables fitting the linear mixed regression model with standard software and hence it simplifies the work of the data analyst. Mean‐squared error estimation that accounts for the uncertainty due to the estimation of the transformation parameters is explored by using the parametric and semiparametric (wild) bootstrap. The methods proposed are illustrated by using real survey and census data for estimating income deprivation parameters for municipalities in the Mexican state of Guerrero. Simulation studies and the results from the application show that using carefully selected, data‐driven transformations can improve small area estimation.

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“…)= 18·911 (0'02), very close to Hinkley's. Carroll & Ruppert (1987) have shown how diagnostics may be used to suggest data transformations to induce homoscedastic errors. However their approach uses traditional diagnostics rather than the high breakdown diagnostics of Rousseeuw & Leroy (1987) and needs separate investigation.…”

Section: Two Numerical Examplesmentioning

confidence: 99%

Robust Regression Estimators-The Choice of Tuning Constants

Kelly¹

1992

The Statistician

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The robust regression estimators of Huber and Welsch and the bounded influence estimators of Krasker and Welsch require the specification of a cut‐off or tuning constant before they are fully defined. Here the asymptotic mean squared errors of these estimators under different designs/distributions for the explanatory variables and different error distribution are computed. The choice of tuning constants seems to be critical in the trade‐off between bias and variance. The choice illuminates the differences in behaviour of the estimators. Rousseeuw's least median of squares estimator is also considered. Two numerical examples further illustrate the differences.

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Diagnostics and Robust Estimation When Transforming the Regression Model and the Response.

Cited by 4 publications

References 1 publication

The Box-Cox Transformation Technique: A Review

The Box-Cox Transformation Technique: A Review

Data-Driven Transformations in Small Area Estimation

Robust Regression Estimators-The Choice of Tuning Constants

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