A vector with n elements that contains
the response variable. y can be either a row or a column vector.
Data Types: single| double
Missing values (NaN's) and infinite values (Inf's) are allowed,
since observations (rows) with missing or infinite values will
automatically be excluded from the computations.
Data Types: single| double
Vector containing initial
estimate of beta (generally an S estimate with high
breakdown point (e.g. 0.5)
Data Types: single| double
Scalar containing estimate of the scale (generally an S
estimate with high breakdown point (e.g. .5)
Data Types: single| double
Specify optional comma-separated pairs of Name,Value arguments.
Name is the argument name and Value
is the corresponding value. Name must appear
inside single quotes (' ').
You can specify several name and value pair arguments in any order as
Name1,Value1,...,NameN,ValueN.
Example:
'intercept',false
, 'eff',0.99
, 'effshape',1
, 'refsteps',10
, 'tol',1e-10
, 'conflev',0.99
, 'rhofunc','optimal'
, 'rhofuncparam',5
, 'nocheck',true
, 'plots',0
, 'yxsave',1
Indicator for the constant term (intercept) in the fit,
specified as the comma-separated pair consisting of
'Intercept' and either true to include or false to remove
the constant term from the model.
Example: 'intercept',false
Data Types: boolean
Scalar defining nominal efficiency (i.e. a number between
0.5 and 0.99). The default value is 0.95
Asymptotic nominal efficiency is:
$(\int \psi' d\Phi)^2 / (\psi^2 d\Phi)$
Example: 'eff',0.99
Data Types: double
If effshape=1 efficiency refers to shape
efficiency else (default) efficiency refers to location
Example: 'effshape',1
Data Types: double
Scalar defining maximum number of iterations in the MM
loop. Default value is 100.
Example: 'refsteps',10
Data Types: double
Scalar controlling tolerance in the MM loop.
Default value is 1e-7
Example: 'tol',1e-10
Data Types: double
Usually conflev=0.95, 0.975 0.99 (individual alpha)
or 1-0.05/n, 1-0.025/n, 1-0.01/n (simultaneous alpha).
Default value is 0.975
Example: 'conflev',0.99
Data Types: double
String which specifies the rho
function which must be used to weight the residuals.
Possible values are
'bisquare';
'optimal';
'hyperbolic';
'hampel';
'mdpd'.
'AS'.
'bisquare' uses Tukey's $\rho$ and $\psi$ functions.
See TBrho and TBpsi.
'optimal' uses optimal $\rho$ and $\psi$ functions.
See OPTrho and OPTpsi.
'hyperbolic' uses hyperbolic $\rho$ and $\psi$ functions.
See HYPrho and HYPpsi.
'hampel' uses Hampel $\rho$ and $\psi$ functions.
See HArho and HApsi.
'mdpd' uses Minimum Density Power Divergence $\rho$ and $\psi$ functions.
See PDrho and PDpsi.
'AS' uses Andrew's sine $\rho$ and $\psi$ functions.
See ASrho and ASpsi.
The default is bisquare
Example: 'rhofunc','optimal'
Data Types: char
For hyperbolic rho function it is possible to set up the
value of k = sup CVC (the default value of k is 4.5).
For Hampel rho function it is possible to define parameters
a, b and c (the default values are a=2, b=4, c=8). For the
other rho functions (Tuhey, PD and optimal) it is an empty
value.
Example: 'rhofuncparam',5
Data Types: single | double
If nocheck is equal to
true no check is performed on matrix y and matrix X. Notice
that y and X are left unchanged. In other words the
additional column of ones for the intercept is not added.
As default nocheck=false.
Example: 'nocheck',true
Data Types: boolean
If plots = 1, generates a plot with the robust residuals
against index number. The confidence level used to draw the
confidence bands for the residuals is given by the input
option conflev. If conflev is not specified a nominal 0.975
confidence interval will be used.
Example: 'plots',0
Data Types: single | double
Default is 0, i.e. no saving is done.
Example: 'yxsave',1
Data Types: double
MMregcore with optional input arguments.