Algorithms, Routines, and S-Functions for Robust Statistics
ROBETH (written in ANSI FORTRAN 77) is a systematized collection of algorithms that allows computation of a broad class of procedures based on M- and high-breakdown point estimation, including robust regression, robust testing of linear hypotheses, and robust coveriances.
This book describes the computational procedures included in ROBETH. Each chapter is organized into three parts:
1. An overview of the theoretical background for the statistical and numerical methods
2. A detailed description of the corresponding FORTRAN subroutines and of the numerical algorithms as they are implemented
3. The scripts of several examples concerning the use of ROBETH by means of the S-PLUS interface, including some examples of high-level S functions.
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Classes of Problems and Robust Methods
Robust Covariance Matrices
Scale in Linear Regression
Weights for Bounded Influence
Covariance Matrix of
Asymptotic Relative Efficiency
Robust Testing in Linear Models
High Breakdown Point Regression
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500 Incorrect input Array of dimension asymptotic coefficient estimates compact storage mode components computation condition constant containing the matrix containing the vector convergence criterion covariance matrix defined denotes design matrix diagonal elements dimension N containing dimension NP distribution Double precision array equation exit FORTRAN go to Step H-algorithm Hampel high breakdown point Householder transformations Huber function Huber-type ICNV Incorrect input parameter initial value INTEGER Integer array ISIGMA ITYPE ITYPE=1 least squares linear lower-triangular matrix M-estimate Mallows Mallows-type MAXIT median absolute deviation Messages 500 Incorrect NITMON NREP Number of columns number of iterations Number of observations Number of rows Option parameter orthogonal matrix outliers output precision specification SUBROUTINE pseudorank regression Remark ROBETH robust routines RYSIGM RYWALG S-PLUS Schweppe Schweppe-type Set NIT Single precision single-parameter external function solution space Subroutines and functions subsamples symmetric matrix THETA User-supplied single-parameter external W Double weight functions XERF