Smoothed rank correlation of the linear transformation regression model

Huazhen Lin, Heng PENG*

*Corresponding author for this work

Research output: Contribution to journalArticlepeer-review

12 Citations (Scopus)

Abstract

The maximum rank correlation (MRC) approach is the most common method used in the literature to estimate the regression coefficients in the semiparametric linear transformation regression model. However, the objective function Gn(β) in the MRC approach is not continuous. The optimization of Gn(β) requires an extensive search for which the computational cost grows in the order of nd, where d is the dimension of X. Given the lack of smoothing, issues related to variable selection, the variance estimate and other inferences by MRC are not well developed in the model. In this paper, we combine the concept underlying the penalized method, rank correlation and smoothing technique and propose a nonconcave penalized smoothed rank correlation method to select variables and estimate parameters for the semiparametric linear transformation model. The proposed estimator is computationally simple, n1 2-consistent and asymptotically normal. A sandwich formula is proposed to estimate the variances of the proposed estimates. We also illustrate the usefulness of the methodology with real data from a body fat prediction study.

Original languageEnglish
Pages (from-to)615-630
Number of pages16
JournalComputational Statistics and Data Analysis
Volume57
Issue number1
DOIs
Publication statusPublished - Jan 2013

Scopus Subject Areas

  • Statistics and Probability
  • Computational Mathematics
  • Computational Theory and Mathematics
  • Applied Mathematics

User-Defined Keywords

  • MRC
  • Semiparametric transformation model
  • Variable selection
  • Variance estimation

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