Abstract
Of the many methods that have been developed for quantile regression (Wright and Royston, 1997) the LMS method (Cole and Green, 1992) can be easily understood, is flexible and based on splines. The basic idea is that, for a fixed value of the covariate, a Box-Cox transformation of the response is applied to obtain standard normality. The three parameters are chosen to maximize a penalized log-likelihood. One unpublished extension by Lopatatzidis and Green is to transform to a gamma distribution, which helps overcome a range-restriction problem in the original formulation. This paper proposes a new method based on the Yeo and Johnson (2000) transformation. It has the advantage that it allows for both positive and negative values in the response. R/S-PLUS software written by the author implementing the LMS method and variants are described and illustrated with data from a New Zealand workforce study.
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Yee, T.W. (2002). An Implementation for Regression Quantile Estimation. In: Härdle, W., Rönz, B. (eds) Compstat. Physica, Heidelberg. https://doi.org/10.1007/978-3-642-57489-4_1
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DOI: https://doi.org/10.1007/978-3-642-57489-4_1
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