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Generalized Rank-Based Estimates for Linear Models with Cluster Correlated Data

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Robust Rank-Based and Nonparametric Methods

Part of the book series: Springer Proceedings in Mathematics & Statistics ((PROMS,volume 168))

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Abstract

This paper focuses on rank-based (R) estimation of parameters in a linear model with cluster correlated errors. The clusters are assumed to be independent, however, within a cluster the responses are allowed to be dependent. The method is applicable to general within cluster error structure. Application of a model which assumes the within cluster errors which follow an AR(1) process is developed. Discussion of an estimate of the AR(1) parameter is included. The algorithm first estimates the correlation structure by obtaining a robust rank-based estimate of the AR(1) parameter. The responses are then transformed to working independence and the model parameters are fit using ordinary rank regression. Estimates of standard errors—which utilize a sandwich estimate—are provided. An example and simulation results are discussed.

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Notes

  1. 1.

    Having bounded influence function and 29 % breakdown point.

  2. 2.

    We do not need the variance to exist. Only that a linear transformation exists which has the goal of reducing the dependence in the response variables. The variance notation is adopted for convenience.

  3. 3.

    As the intercept was fit in the previous step, the residuals should have location zero.

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Author information

Authors and Affiliations

  1. Department of Biostatistics, University of Wisconsin School of Medicine and Public Health, Madison, WI, 53726, USA

    John Kloke

Authors
  1. John Kloke
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Corresponding author

Correspondence to John Kloke .

Editor information

Editors and Affiliations

  1. Department of Statistics, Rutgers University, New Brunswick, New Jersey, USA

    Regina Y. Liu

  2. Department Statistics, Western Michigan University, Kalamazoo, Michigan, USA

    Joseph W. McKean

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Kloke, J. (2016). Generalized Rank-Based Estimates for Linear Models with Cluster Correlated Data. In: Liu, R., McKean, J. (eds) Robust Rank-Based and Nonparametric Methods. Springer Proceedings in Mathematics & Statistics, vol 168. Springer, Cham. https://doi.org/10.1007/978-3-319-39065-9_3

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