Multiple testing procedure for ordered variable selection
Description
Performs multiple hypotheses testing for ordered variable selection.
Usage
1 
Arguments
data 
Input matrix of dimension n * p; each of the n rows is an observation vector of p variables. The intercept should be included in the first column as (1,...,1). If not, it is added. 
Y 
Response variable of length n. 
ordre 
Vector from which the varibles are to be ordered, it can be a partial order. If absent, data is considers to be already ordered; Default is (1,2,..,p). 
var_nonselect 
Number of variables that don't undergo feature selection. They have to be in the first columns of 
alpha 
A user supplied type I error sequence. Default is 
IT 
Number of simulations in the calculation of the quantile. Default is 10000. 
sigma 
Value of the variance if it is known; 0 otherwise. Default is 0. 
showresult 
Logical value. if TRUE, shows the value of the statistics and the estimated quantile at each step of the procedure. Default is TRUE. 
Details
The details of the procedure are in 'Multiple hypotheses testing for variable selection; F. Rohart 2011'. If showresult
=TRUE, the statistics and quantile are printed through the algorithm. If the statistic is greater than the quantile, the test is rejected (takes the value 1). The procedure stops when the null huypothesis is accepted (all alternative hypotheses are 0).
The statistics to test the null hypotheses are different whether the variance sigma
is known.
Value
A 'mht.order' object is returned for which the methods predict
, refit
and plot
are available.
data 
A list containing:

coefficients 
Matrix of the estimated coefficients. Each row concerns a specific user level 
residuals 
Matrix of the residuals. Each row concerns a specific user level 
relevant_var 
Set of the relevant variables. Each row concerns a specific user level 
fitted.values 
Matrix of the fitted values, each column concerns a specific user level 
kchap 
Vector containing the length of the estimated set of relevant variables, for each values of 
quantile 
The estimated type I error to be used in the second step of the procedure in order to have a test of level alpha, each column stands for one test. See F.Rohart (2011) for details. 
call 
The call that has been used. 
References
Adaptive tests of linear hypotheses by model selection; Baraud & al 2002
Multiple hypotheses testing for variable selection; F. Rohart 2011
See Also
predict.mht.order
, refit.mht.order
, plot.mht.order
Examples
1 2 3 4 5 6 7 8 9 