Response variable, specified as
a vector of length n, where n is the number of
observations. Each entry in y is the response for the
corresponding row of X.
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
Matrix of explanatory variables (also called 'regressors')
of dimension n x (p-1) where p denotes the number of
explanatory variables including the intercept.
Rows of X represent observations, and columns represent
variables. By default, there is a constant term in the
model, unless you explicitly remove it using input option
intercept, so do not include a column of 1s in X. 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
n x r matrix or vector of length r.
If Z is a n x r matrix it contains the r variables which
form the scedastic function as follows (if input option art==1)
\[
\omega_i = 1 + exp(\gamma_0 + \gamma_1 Z(i,1) + ...+ \gamma_{r} Z(i,r))
\]
If Z is a vector of length r it contains the indexes of the
columns of matrix X which form the scedastic function as
follows
\[
\omega_i = 1 + exp(\gamma_0 + \gamma_1 X(i,Z(1)) + ...+
\gamma_{r} X(i,Z(r)))
\]
Therefore, if for example the explanatory variables
responsible for heteroscedasticity are columns 3 and 5
of matrix X, it is possible to use both the sintax
FSRHmdr(y,X,X(:,[3 5]),0)
or the sintax
FSRHmdr(y,X,[3 5],0)
Data Types: single| double
If
bsb=0 then the procedure starts with p units randomly
chosen else if bsb is not 0 the search will start with
m0=length(bsb)
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:
'init',100 starts monitoring from step m=100
, 'intercept',false
, 'typeH','har'
, 'plots',1
, 'nocheck',true
, 'msg',1
, 'gridsearch',0
, 'constr',[1 6 3]
, 'bsbmfullrank',0
,
It specifies the point where to start monitoring
required diagnostics. If it is not specified it is set
equal to:
p+1, if the sample size is smaller than 40;
min(3*p+1,floor(0.5*(n+p+1))), otherwise.
The minimum value of init is 0. In this case in the first
step we just use prior information
Example: 'init',100 starts monitoring from step m=100
Data Types: double
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
If typeH is 'art' (default) than the skedastic function is
modelled as follows
\[
\sigma^2_i = \sigma^2 (1 + \exp(\gamma_0 + \gamma_1 Z(i,1) +
\cdots + \gamma_{r} Z(i,r)))
\]
on the other hand, if typeH is 'har' then traditional
formulation due to Harvey is used as follows
\[
\sigma^2_i = \exp(\gamma_0 + \gamma_1 Z(i,1) + \cdots +
\gamma_{r} Z(i,r)) =\sigma^2 (\exp(\gamma_1
Z(i,1) + \cdots + \gamma_{r} Z(i,r))
\]
Example: 'typeH','har'
Data Types: character or string
If equal to one a plot of Bayesian minimum deletion
residual appears on the screen with 1 per cent, 50 per
cent and 99 per cent confidence bands else (default) no
plot is shown.
Remark. the plot which is produced is very simple. In order
to control a series of options in this plot and in order to
connect it dynamically to the other forward plots it is necessary to use
function mdrplot
Example: 'plots',1
Data Types: 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
It controls whether to display or not messages
about great interchange on the screen
If msg==1 (default) messages are displyed on the screen
else no message is displayed on the screen
Example: 'msg',1
Data Types: double
If gridsearch ==1 grid search will be used else the
scoring algorith will be used.
REMARK: the grid search has only been implemented when
there is just one explantory variable which controls
heteroskedasticity.
Example: 'gridsearch',0
Data Types: double
r x 1 vector. The default is constr=''. No constraint is imposed
Example: 'constr',[1 6 3]
Data Types: double
In other words, this options controls what to do when rank(X(bsbm,:)) is
smaller then number of explanatory variables. If
bsbmfullrank = 1 (default is 1) these units (whose number is
say mnofullrank) are constrained to enter the search in
the final n-mnofullrank steps else the search continues
using as estimate of beta at step m the estimate of beta
found in the previous step.
Example: 'bsbmfullrank',0
Data Types: double
It specifies for which steps of the fwd search it is
necessary to save the units forming subset. If bsbsteps is
0 we store the units forming subset in all steps. The
default is store the units forming subset in all steps if
n<=5000, else to store the units forming subset at steps
init and steps which are multiple of 100. For example, as
default, if n=7530 and init=6, units forming subset are
stored for
m=init, 100, 200, ..., 7500.
Example: 'bsbsteps',[100 200] stores the unis forming
subset in steps 100 and 200.
Data Types: double
FSRHmdr with all default options.