Computational Statistics and Data Analysis 78 (2014) 186–205

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To alleviate the computational burden of making the relevant estimation algorithms stable
for nonlinear and semiparametric regression models with, particularly, high-dimensional
data, a transformation-based method combining sufficient dimension reduction approach
is proposed. To this end, model-independent transformations are introduced to models under
study. This generic methodology can be applied to transformation models; generalized
linear models; and their corresponding quantile regression variants. The constructed estimates
almost have closed forms in certain sense such that the above goals can be achieved.
Simulation results show that, in finite sample cases with high-dimensional predictors and
long-tailed distributions of error, the new estimates often exhibit a smaller degree of variance,
and have much less computational burden than the classical methods such as the
classical least squares and quantile regression estimation.

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Keywords: Generalized linear model Model-independent transformation Quantile regression Transformation model