# R Functions for Robust Statistics

## Documentation for package ‘robeth’ version 2.7-6

- DESCRIPTION file.

## Help Pages

A B C D E F G H I K L M N P Q R S T U V W X Z

robeth-package | Interface for the FORTRAN programs developed at the ETH-Zuerich and then at IUMSP-Lausanne

## -- A --

addc | Adds a column vector to a transformed design matrix and updates its QR-decomposition
airef0 | Asymptotic relative efficiency of a general M-estimate for a model with mu quantitative covariates with or without a constant term
airefq | Asymptotic relative efficiency of a general M-estimate for a model with mu quantitative and nu qualitative covariates

## -- B --

binprd | Binomial probability distribution

## -- C --

cerf | Complemented error function (single precision)
cerfd | Complemented error function (double precision)
cfrcov | Computation of fC.fC.inv(AT A) for a given matrix A and scale factor fC
Chi | Chi weight function for location and regression
chi | Chi weight function for location and regression
chisq | Cumulative Chi-square distribution function
cia2b2 | Determination of the parameters a2 and b2 of the Huber weight function from the proportion eps of contamination
cibeat | Determination of the parameter d of the Huber weight function
cicloc | Determination of the parameter c of the Huber weight function from the proportion eps of contamination
cifact | Determination of the correction factor for the M-estimate based on Huber weight function
cimedv | Initial values for the iterative algorithms implemented in CYFALG, CYNALG, and CYGALG
cirock | Initial values for the Rocke estimates of covariance
comval | Gives the current values ofthe parameters of the ROBETH subroutine common blocks
cquant | Inverse of the cumulative Chi2-distribution function
cyfalg | Fixed-point algorithm for the computation of an M-estimate of multivariate location and scatter
cygalg | Conjugate gradient algorithm for the computation of an M-estimate of multivariate location and scatter
cynalg | Newton-type algorithm for the computation of an M-estimate of multivariate location and scatter

## -- D --

Dbinom | Diagonal matrix D for the binomial case in discrete GLM
dfcomn | Assigns values to the ROBETH parameters included in common blocks
dfrpar | Sets default parameters for regression estimates
dfvals | Provide default values for most scalar parameters used by the Robeth subroutines
dotp | Forms the scalar (dot) product of two vectors
dotpd | Forms the scalar (dot) product of two vectors (double precision)
dpoiss | Diagonal matrix D for the Poisson case in discrete GLM

## -- E --

exch | Exchanges two columns of a symmetric matrix
exchd | Exchanges two columns of a symmetric matrix (double precision)

## -- F --

fcum | Cumulative F-distribution function
Fn.Exp.f | Parametric estimate of survival cdf
fstord | Determination of the j-th order statistic

## -- G --

gauss | Cumulative Gaussian distribution function
gaussd | Cumulative Gaussian distribution function (double precision)
gfedca | Diagonal matrices D_G and E_G
gintac | Initial values of theta, A and c_i,...,c_n
glmdev | The total deviance of the fitted generalizrd linear model
gyastp | Fixed-point algorithm for the A-step
gycstp | Newton-type algorithm for the c-step
gymain | Main algorithm
gytstp | Newton-type algorithm for the theta-step

## -- H --

h12 | Constructs and/or applies a single elementary Householder transformation
h12d | Constructs and/or applies a single elementary Householder transformation (double precision)
hylmse | Resampling algorithm for the computation of the LMS estimate
hyltse | Resampling algorithm for the computation of the LTS estimate
hysest | Resampling algorithm for the computation of S-estimates
hysestw | Resampling algorithm for the computation of weighted S-estimates

## -- I --

ingama | Incomplete Gamma-integral function

## -- K --

kfascv | Backtransformation of the covariance matrix of the coefficient estimates
kfedcb | Diagonal hat matrices D_M, E_M, D_S, and E_S
kfedcc | Diagonal 'check' matrices D_M, E_M, D_S, and E_S
kffacv | Correction factor f_H for the covariance matrix of a Huber-type estimate
kiascv | Covariance matrix of the coefficient estimates of the form f.inv(XT X) in the transformed coordinate system
kiedch | Diagonal matrices D_M, E_M, D_S, E_S when psi is the Huber function
kiedcu | Diagonal matrices D_M, E_M, D_S, E_S when psi is a user-supplied function
ktaskv | Covariance matrix of the coefficient estimates of the form f.inv(XT X)
ktaskw | Covariance matrix of the coefficient estimates of the form f.inv(S1) S2 inv(S1)

## -- L --

lgama | Logarithm at the Gamma-function at the point x
libet0 | Computation of Beta0 = Phi_inv(0.75)
libeth | Computation of Int Chi(s) dPhi(s) when Chi=Psi.Psi/2 and Psi is the Huber function
libetu | Computation of Int Chi(s) dPhi(s) when Chi is a user-supplied function
liclls | Classical estimates of mean and standard deviation
liepsh | Computation of Int Psi(s).Psi(s) dPhi(s) and Int Psi'(s) dPhi(s) when Psi is the Huber function
liepsu | Computation of Int Psi(s).Psi(s) dPhi(s) and Int Psi'(s) dPhi(s) when Psi is a user-supplied external function
liindh | Inverts the approximate null distribution of the one-sample Wilcoxon test statistic
liinds | Inverts the approximate null distribution of the sign test statistic
liindw | Inverts the approximate null distribution of the Mann-Whitney test statistic
lilars | Median an median absolute deviation
littst | t-test for the shift parameter
lmdd | Median and median absolute deviation
lrfctd | Computation of Li, li and lip
lyhalg | M-estimate of location with simultaneous estimation of scale
lyhdle | Hodges-Lehman estimate and confidence intervals for the center of symmetry based on the one-sample Wilcoxon test
lymnwt | Nonparametric estimate and confidence intervals for the shift parameter based on the Mann-Whitney test statistic
lytau2 | tau-test for the shift parameter
lywalg | W-algorithm for M-estimate of location

## -- M --

mchl | Cholesky decomposition of a symmetric matrix
mchld | Cholesky decomposition of a symmetric matrix (double precision)
messagena | Print a message when a required argument is missing
mff | Multiplies a full matrix by a full matrix
mffd | Multiplies a full matrix by a full matrix (double precision)
mfragr | Generation and comparison of all regressions on subsets of covariates
mfy | Multiplies a full matrix by a vector
mfyd | Multiplies a full matrix by a vector (double precision)
mhat | Computes the diagonal elements of the hat matrix
minv | Inverts a triangular matrix
minvd | Inverts a triangular matrix (double precision)
mirtsr | Computation of (robust) t-statistics for t-directed search
mly | Multiplies a lower-triangular matrix by a vector
mlyd | Multiplies a lower-triangular matrix by a vector (double precision)
msf | Multiplies a symmetric matrix by a full matrix
msf1 | Multiplies a symmetric matrix by a full matrix when the result is a symmetric matrix
msf1d | Multiplies a symmetric matrix by a full matrix when the result is a symmetric matrix
msfd | Multiplies a symmetric matrix by a full matrix (double precision)
mss | Multiplies a symmetric matrix by a symmetric matrix
mssd | Multiplies a symmetric matrix by a symmetric matrix (double precision)
mtt1 | Multiplies an upper-triangular matrix by its transpose
mtt1d | Multiplies an upper-triangular matrix by its transpose (double precision)
mtt2 | Multiplies a lower-triangular matrix by its transpose
mtt2d | Multiplies a lower-triangular matrix by its transpose (double precision)
mtt3 | Multiplies a triangular matrix by a triangular matrix
mtt3d | Multiplies a triangular matrix by a triangular matrix (double precision)
mty | Multiplies an upper-triangular matrix by a vector
mtyd | Multiplies an upper-triangular matrix by a vector
myhbhe | High breakdown point and high efficiency regression with test for bias
mymvlm | Simultaneous computation of the MVE and LMS estimates

## -- N --

nlgm | Logarithm of the Gamma-function at the point n/2
nrm2 | Forms the Euclidean norm of a vector
nrm2d | Forms the Euclidean norm of a vector (double precision)

## -- P --

permc | Permutes the columns of a matrix by means of transpositions
permv | Permutes the elements of a vector
poissn | Poisson distribution
precd | Algorithmic determination of the smallest double precision positive number x
precs | Algorithmic determination of the smallest double precision positive number x
probst | Cumulative t-distribution function
Psi | psi weight function for location and regression
psi | psi weight function for location and regression
Psp | psi' weight function for location and regression
psp | psi' weight function for location and regression

## -- Q --

QD2coef.f | Auxiliary function to find mu and sigma parameter for extended loggamma distribution
QD2funC.f | Auxiliary function to find lambda parameter for extended loggamma distribution
Qn.Exp.f | Auxiliary function to compute quantiles of survival cdf
quant | Inverse of the standard Gaussian cumulative distribution function

## -- R --

Random | Uniform random number generator
Regtau.f | Auxiliary function for the computation of QQopt
RegtauW.f | Auxiliary function for the computation of QQopt
Rho | Rho weight function for location and regression
rho | rho weight function for location and regression
ribet0 | Computation of the constant Beta0
ribeth | Computation of the constant Beta when Chi=Psi.Psi/2 and Psi is the Huber function
ribetu | Computation of the constant Beta when Chi is a user-supplied function
riclls | Solution of the least squares problem
rilars | Solution of the least absolute residual problem
rimtrd | Double precision version of RIMTRF
rimtrf | Upper triangularization (QR-decomposition) of the design matrix and determination of its pseudorank
rmvc | Removes a column from a transformed design matrix and updates its QR-decomposition
robeth | Interface for the FORTRAN programs developed at the ETH-Zuerich and then at IUMSP-Lausanne
ruben | Cumulative distribution and density function of a linear combination of chi-2 random variables
rybifr | Bounded influence regression
ryhalg | H-algorithm for M-estimates
rynalg | Newton algorithm with adaptive steps for M-estimates
rysalg | S-algorithm for M-estimates
rysigm | Iterative algorithm for the computation of an M-estimate of the scale parameter when the residuals are given
rywalg | W-algorithm for M-estimates

## -- S --

scal | Scales a vector by a constant
scald | Scales a double precision vector by a constant
srt1 | Sorts the components of a vector in ascending order
srt2 | Sorts the components of a vector in ascending order and permutes the components of another vector accordingly
swap | Interchanges two vectors
swapd | Interchanges two vectors (double precision)

## -- T --

tauare | Asymptotic relative efficiency of the tau-test
tfrn2t | Computes the Rn2-test statistic for a linear hypothesis in canonical form
tftaut | Computes the tau-test statistic for a linear hypothesis in canonical form
tisrtc | Permutes the columns of the design matrix: Predictors in omega are placed in the first q positions
to.character | Convert local variable to Fortran character
to.double | Convert local variable to Fortran double precision
to.integer | Convert local variable to Fortran integer
to.single | Convert local variable to Fortran single precision
tquant | Inverse of the cumulative t-distribution function
ttaskt | Computes the matrix Ktau
tteign | Computes the eigenvalues of the matrix Ktau

## -- U --

Ucv | u weight function for covariances
ucv | u weight function for covariances
ugl | ub weight function for M-estimates in GLM
Upcv | u' weight function for covariances
upcv | u' weight function for covariances
userfd | Dummy u user function (double precision)
userfs | Dummy u user function

## -- V --

vcv | v weight function for covariances
vpcv | v' weight function for covariances

## -- W --

Wcv | w weight function for covariances
wcv | v weight function for covariances
wfshat | Schweppe original weight proposal
wimedv | Initial value of the matrix A
Wpcv | w' weight function for covariances
wpcv | w' weight function for covariances
Www | w weight function for covariances
www | w weight function
wyfalg | Fixed-point algorithm for the computation of the matrix A
wyfcol | Modified fixed-point algorithm for collinear data in the standardized case
wygalg | Conjugate gradient algorithm for the computation of the lower-triangular matrix A in the standardized case
wynalg | Newton-Huber algorithm for the computation of the lower-triangular matrix A in the standardized case

## -- X --

xerf | Gaussian density function
xerp | Density of the norm of a standard Gaussian vector with p components
xsy | Evaluates a quadratic form
xsyd | Evaluates a quadratic form (double precision)

## -- Z --

zemll | Zeng method for censored data