Transforming response values in small area prediction

Kubokawa, Tatsuya

doi:10.1016/j.csda.2017.03.017

Cited by 25 publications

(19 citation statements)

References 35 publications

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“…Slud and Maiti (2006)) and data-driven transformations (e.g. Sugasawa and Kubokawa (2017)). Rojas-Perilla et al (2020) presented theoretical and numerical justifications for the use of data-driven transformations with unit-level SAE models.…”

Section: Introductionmentioning

confidence: 99%

Domain Prediction with Grouped Income Data

Walter

Groß

Schmid

et al. 2021

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

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Section: Introductionmentioning

confidence: 99%

Domain Prediction with Grouped Income Data

Walter

Groß

Schmid

et al. 2021

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

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“…Equation (1) is estimated using θ true^ d * as the direct estimate and var( θ true^ d * ) as the estimate for the sampling error variance. To bring the estimated EBLUP and MSE back from the transformed to the original scale, we advise a bias correction (Slud and Maiti 2006; Sugawasa and Kubokawa 2017). includes two back-transformation methods: the “crude” method, shown in Neves, Silva, and Correa (2013) and Rao and Molina (2015), and (as the default) the bias correction proposed by Slud and Maiti (2006).…”

Section: The Fh Modelmentioning

confidence: 99%

The fayherriot command for estimating small-area indicators

Halbmeier

Kreutzmann

Schmid

et al. 2019

The Stata Journal: Promoting communications on statistics and S

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We introduce a command, fayherriot, that implements the Fay– Herriot model (Fay and Herriot, 1979, Journal of the American Statistical Association 74: 269–277), which is a small-area estimation technique (Rao and Molina, 2015, Small Area Estimation), in Stata. The Fay–Herriot model improves the precision of area-level direct estimates using area-level covariates. It belongs to the class of linear mixed models with normally distributed error terms. The fayherriot command encompasses options to a) produce out-of-sample predictions, b) adjust nonpositive random-effects variance estimates, and c) deal with the violation of model assumptions.

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“…The DP transformation is described as

H_{λ}^{DP} false(x false) = \frac{x^{λ} - x^{- λ}}{2 λ}, x > 0, λ > 0,

where

\lim_{λ \to 0} H_{λ}^{DP} false(x false) = \log x

. In the context of small area estimation, the classical Fay–Herriot model has been extended by Sugasawa and Kubokawa () with the use of DP transformation. It is easy to confirm that the range of DP transformation is

double-struckR

.…”

Section: Adaptively Transformed Mixed‐model Predictionmentioning

confidence: 99%

Adaptively transformed mixed‐model prediction of general finite‐population parameters

Kubokawa

2019

Scandinavian J Statistics

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For estimating area‐specific parameters (quantities) in a finite population, a mixed‐model prediction approach is attractive. However, this approach strongly depends on the normality assumption of the response values, although we often encounter a non‐normal case in practice. In such a case, transforming observations to make them suitable for normality assumption is a useful tool, but the problem of selecting a suitable transformation still remains open. To overcome the difficulty, we here propose a new empirical best predicting method by using a parametric family of transformations to estimate a suitable transformation based on the data. We suggest a simple estimating method for transformation parameters based on the profile likelihood function, which achieves consistency under some conditions on transformation functions. For measuring the variability of point prediction, we construct an empirical Bayes confidence interval of the population parameter of interest. Through simulation studies, we investigate the numerical performance of the proposed methods. Finally, we apply the proposed method to synthetic income data in Spanish provinces in which the resulting estimates indicate that the commonly used log transformation would not be appropriate.

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Transforming response values in small area prediction

Cited by 25 publications

References 35 publications

Domain Prediction with Grouped Income Data

Domain Prediction with Grouped Income Data

The fayherriot command for estimating small-area indicators

Adaptively transformed mixed‐model prediction of general finite‐population parameters

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