# Rank-based Estimates of Regression Coefficients

### Description

Minimizes Jaeckel's dispersion function to obtain a rank-based solution for linear models.

### Usage

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### Arguments

`formula` |
an object of class formula |

`data` |
an optional data frame |

`subset` |
an optional argument specifying the subset of observations to be used |

`yhat0` |
an n by vector of initial fitted values, default is NULL |

`scores` |
an object of class 'scores' |

`symmetric` |
logical. If 'FALSE' uses median of residuals as estimate of intercept |

`TAU` |
version of estimation routine for scale parameter. F0 for Fortran, R for (slower) R, N for none |

`...` |
additional arguments to be passed to fitting routines |

### Details

Rank-based estimation involves replacing the L2 norm of least squares estimation with a pseudo-norm which is a function of the ranks of the residuals.
That is, in rank estimation, the usual notion of Euclidean distance is replaced with another measure of distance which is referred to as Jaeckel's (1972) dispersion function.
Jaeckel's dispersion function depends on a score function and a library of commonly used score functions is included. e.g. Wilcoxon and sign score functions.
If an inital fit is not supplied (i.e. yhat0 = NULL) then inital fit is based on an LS fit via `lm`

.

### Value

`coefficients` |
estimated regression coefficents with intercept |

`residuals` |
the residuals, i.e. y-yhat |

`fitted.values` |
yhat = x betahat |

`xc` |
centered design matrix |

`tauhat` |
estimated value of the scale parameter tau |

`taushat` |
estimated value of the scale parameter tau_s |

`betahat` |
estimated regression coefficents |

`call` |
Call to the function |

### Author(s)

John Kloke kloke@biostat.wisc.edu

### References

Hettmansperger, T.P. and McKean J.W. (2011), *Robust Nonparametric Statistical Methods, 2nd ed.*, New York: Chapman-Hall.

Jaeckel, L. A. (1972). Estimating regression coefficients by minimizing the dispersion of residuals. *Annals of Mathematical Statistics*, 43, 1449 - 1458.

Jureckova, J. (1971). Nonparametric estimate of regression coefficients. *Annals of Mathematical Statistics*, 42, 1328 - 1338.

### See Also

`summary.rfit`

### Examples

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