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Rank-Based Analysis of Linear Models Using R

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  • Terpstra, Jeff T.
  • McKean, Joseph W.

Abstract

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.

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  • Terpstra, Jeff T. & McKean, Joseph W., 2005. "Rank-Based Analysis of Linear Models Using R," Journal of Statistical Software, Foundation for Open Access Statistics, vol. 14(i07).
    • Handle: RePEc:jss:jstsof:v:014:i07
    DOI: http://hdl.handle.net/10.18637/jss.v014.i07
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    References listed on IDEAS

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    1. Koenker, Roger W & Bassett, Gilbert, Jr, 1978. "Regression Quantiles," Econometrica, Econometric Society, vol. 46(1), pages 33-50, January.
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    Cited by:

    1. Roelant, E. & Van Aelst, S. & Croux, C., 2009. "Multivariate generalized S-estimators," Journal of Multivariate Analysis, Elsevier, vol. 100(5), pages 876-887, May.
    2. Long Feng & Changliang Zou & Zhaojun Wang & Xianwu Wei & Bin Chen, 2015. "Robust spline-based variable selection in varying coefficient model," Metrika: International Journal for Theoretical and Applied Statistics, Springer, vol. 78(1), pages 85-118, January.
    3. Long Feng & Changliang Zou & Zhaojun Wang & Lixing Zhu, 2015. "Robust comparison of regression curves," TEST: An Official Journal of the Spanish Society of Statistics and Operations Research, Springer;Sociedad de Estadística e Investigación Operativa, vol. 24(1), pages 185-204, March.
    4. Wang, Haiyan & Maldonado, Diego & Silwal, Sharad, 2011. "A nonparametric-test-based structural similarity measure for digital images," Computational Statistics & Data Analysis, Elsevier, vol. 55(11), pages 2925-2936, November.
    5. Yang, Hu & Guo, Chaohui & Lv, Jing, 2015. "SCAD penalized rank regression with a diverging number of parameters," Journal of Multivariate Analysis, Elsevier, vol. 133(C), pages 321-333.
    6. Feng, Long & Zou, Changliang & Wang, Zhaojun, 2012. "Local Walsh-average regression," Journal of Multivariate Analysis, Elsevier, vol. 106(C), pages 36-48.
    7. Zhang, Qingzhao & Duan, Xiaogang & Ma, Shuangge, 2017. "Focused information criterion and model averaging with generalized rank regression," Statistics & Probability Letters, Elsevier, vol. 122(C), pages 11-19.
    8. repec:jss:jstsof:43:i05 is not listed on IDEAS
    9. Liya Fu & Zhuoran Yang & Yan Zhou & You-Gan Wang, 2021. "An efficient Gehan-type estimation for the accelerated failure time model with clustered and censored data," Lifetime Data Analysis: An International Journal Devoted to Statistical Methods and Applications for Time-to-Event Data, Springer, vol. 27(4), pages 679-709, October.
    10. Lan Wang & Runze Li, 2009. "Weighted Wilcoxon-Type Smoothly Clipped Absolute Deviation Method," Biometrics, The International Biometric Society, vol. 65(2), pages 564-571, June.
    11. Melody Denhere & Huybrechts F. Bindele, 2016. "Rank estimation for the functional linear model," Journal of Applied Statistics, Taylor & Francis Journals, vol. 43(10), pages 1928-1944, August.

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