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Transformation Models in High-Dimensions

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  • Sven Klaassen
  • Jannis Kueck
  • Martin Spindler

Abstract

Transformation models are a very important tool for applied statisticians and econometricians. In many applications, the dependent variable is transformed so that homogeneity or normal distribution of the error holds. In this paper, we analyze transformation models in a high-dimensional setting, where the set of potential covariates is large. We propose an estimator for the transformation parameter and we show that it is asymptotically normally distributed using an orthogonalized moment condition where the nuisance functions depend on the target parameter. In a simulation study, we show that the proposed estimator works well in small samples. A common practice in labor economics is to transform wage with the log-function. In this study, we test if this transformation holds in CPS data from the United States.

Suggested Citation

  • Sven Klaassen & Jannis Kueck & Martin Spindler, 2017. "Transformation Models in High-Dimensions," Papers 1712.07364, arXiv.org.
    • Handle: RePEc:arx:papers:1712.07364
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    References listed on IDEAS

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    1. Victor Chernozhukov & Denis Chetverikov & Mert Demirer & Esther Duflo & Christian Hansen & Whitney Newey & James Robins, 2018. "Double/debiased machine learning for treatment and structural parameters," Econometrics Journal, Royal Economic Society, vol. 21(1), pages 1-68, February.
    2. Neumeyer, Natalie & Noh, Hohsuk & Van Keilegom, Ingrid, 2016. "Heteroscedastic semiparametric transformation models: estimation and testing for validity," LIDAM Reprints ISBA 2016021, Université catholique de Louvain, Institute of Statistics, Biostatistics and Actuarial Sciences (ISBA).
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    6. Victor Chernozhukov & Denis Chetverikov & Mert Demirer & Esther Duflo & Christian Hansen & Whitney Newey, 2017. "Double/Debiased/Neyman Machine Learning of Treatment Effects," American Economic Review, American Economic Association, vol. 107(5), pages 261-265, May.
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