Rank-Based Analysis of Linear Models Using R. It is well-known that Wilcoxon procedures out perform least squares procedures when the data deviate from normality and/or contain outliers. These procedures can be generalized by introducing weights; yielding so-called weighted Wilcoxon (WW) techniques. In this paper we demonstrate how WW-estimates can be calculated using an L1 regression routine. More importantly, we present a collection of functions that can be used to implement a robust analysis of a linear model based on WW-estimates. For instance, estimation, tests of linear hypotheses, residual analyses, and diagnostics to detect differences in fits for various weighting schemes are discussed. We analyze a regression model, designed experiment, and autoregressive time series model for the sake of illustration. We have chosen to implement the suite of functions using the R statistical software package. Because R is freely available and runs on multiple platforms, WW-estimation and associated inference is now universally accessible.

References in zbMATH (referenced in 21 articles , 1 standard article )

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  1. Fu, Liya; Yang, Zhuoran; Cai, Fengjing; Wang, You-Gan: Efficient and doubly-robust methods for variable selection and parameter estimation in longitudinal data analysis (2021)
  2. Fu, Liya; Yang, Zhuoran; Zhou, Yan; Wang, You-Gan: An efficient Gehan-type estimation for the accelerated failure time model with clustered and censored data (2021)
  3. Yang, Jing; Lu, Fang; Yang, Hu: Local Walsh-average-based estimation and variable selection for single-index models (2019)
  4. Auda, Hend A.; Ismail, Mohamed A.; Rashed, Ali A.: Wilcoxon rank based principal component analysis (2018)
  5. Du, Jiang; Chen, Xiuping; Kwessi, Eddy; Sun, Zhimeng: Model averaging based on rank (2018)
  6. Du, Jiang; Zhang, Zhongzhan; Xie, Tianfa: Model averaging for M-estimation (2018)
  7. Zhang, Qingzhao; Duan, Xiaogang; Ma, Shuangge: Focused information criterion and model averaging with generalized rank regression (2017)
  8. Zhang, Qing Zhao; Duan, Xiao Gang; Zhou, Xiao Hua: A weighted Wilcoxon estimate for the covariate-specific ROC curve (2017)
  9. Denhere, Melody; Bindele, Huybrechts F.: Rank estimation for the functional linear model (2016)
  10. Feng, Long; Zou, Changliang; Wang, Zhaojun; Wei, Xianwu; Chen, Bin: Robust spline-based variable selection in varying coefficient model (2015)
  11. Feng, Long; Zou, Changliang; Wang, Zhaojun; Zhu, Lixing: Robust comparison of regression curves (2015)
  12. Yang, Hu; Guo, Chaohui; Lv, Jing: SCAD penalized rank regression with a diverging number of parameters (2015)
  13. Zhu, Neng-Hui: Two-stage local Walsh average estimation of generalized varying coefficient models (2015)
  14. Feng, Long; Zou, Changliang; Wang, Zhaojun: Local Walsh-average regression (2012)
  15. Wang, Haiyan; Tolos, Siti; Wang, Suojin: A distribution free test to detect general dependence between a response variable and a covariate in the presence of heteroscedastic treatment effects (2010)
  16. Roelant, E.; van Aelst, S.; Croux, C.: Multivariate generalized S-estimators (2009)
  17. Gao, Xin; Alvo, Mayer: Nonparametric multiple comparison procedures for unbalanced two-way layouts (2008)
  18. Gao, Xin; Alvo, Mayer; Chen, Jie; Li, Gang: Nonparametric multiple comparison procedures for unbalanced one-way factorial designs (2008)
  19. Omelka, Marek: Second-order linearity of Wilcoxon statistics (2007)
  20. Jeff Terpstra; Joseph McKean: Rank-Based Analysis of Linear Models Using R (2005) not zbMATH

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