fsreda.object {fsdaR}

Description of fsreda Objects

Description

An object of class fsreda.object holds information about the result of a call to fsreg.

Value

The object itself is basically a list with the following components:

RES

n x (n-init+1) matrix containing the monitoring of scaled residuals: the first row is the residual for the first unit, ..., n-th row is the residual for the n-th unit.

LEV

(n+1) x (n-init+1) matrix containing the monitoring of leverage: the first row is the leverage for the first unit, ..., n-th row is the leverage for the n-th unit.

BB

n x (n-init+1) matrix containing the information about the units belonging to the subset at each step of the forward search: first col contains indexes of the units forming subset in the initial step; ...; last column contains units forming subset in the final step (all units).

mdr

n-init x 3 matrix which contains the monitoring of minimum deletion residual or (m+1)-ordered residual at each step of the forward search: first col is the fwd search index (from init to n-1); 2nd col = minimum deletion residual; 3rd col = (m+1)-ordered residual.

Remark: these quantities are stored with sign, that is the min deletion residual is stored with negative sign if it corresponds to a negative residual.

msr

n-init+1 x 3 matrix which contains the monitoring of maximum studentized residual or m-th ordered residual: first col is the fwd search index (from init to n); 2nd col = maximum studentized residual; 3rd col = (m)-ordered studentized residual.

nor

(n-init+1) x 4 matrix containing the monitoring of normality test in each step of the forward search: first col = fwd search index (from init to n); 2nd col = Asymmetry test; 3rd col = Kurtosis test; 4th col = Normality test.

Bols

(n-init+1) x (p+1) matrix containing the monitoring of estimated beta coefficients in each step of the forward search.

S2

(n-init+1) x 5 matrix containing the monitoring of S2 or R2 and F-test in each step of the forward search:

1. 1st col = fwd search index (from init to n);

2. 2nd col = monitoring of S2;

3. 3rd col = monitoring of R2;

4. 4th col = monitoring of rescaled S2. In this case the estimated of sigma^2 at step m is divided by the consistency factor (to make the estimate asymptotically unbiased)

5. 5th col = monitoring of F test. Note that an asymptotic unbiased estimate of sigma^2 is used.

In this case the estimated of s2 at step m is divided by the consistency factor (to make the estimate asymptotically unbiased).

coo

(n-init+1) x 3 matrix containing the monitoring of Cook or modified Cook distance in each step of the forward search:

1. 1st col = fwd search index (from init to n);

2. 2nd col = monitoring of Cook distance;

3. 3rd col = monitoring of modified Cook distance.

Tols

(n-init+1) x (p+1) matrix containing the monitoring of estimated t-statistics (as specified in option input 'tstat') in each step of the forward search

Un

(n-init) x 11 matrix which contains the unit(s) included in the subset at each step of the fwd search.

REMARK: in every step the new subset is compared with the old subset. Un contains the unit(s) present in the new subset but not in the old one Un(1,2) for example contains the unit included in step init+1 Un(end,2) contains the units included in the final step of the search.

betaINT

Confidence intervals for the elements of β. betaINT is a (n-init+1)-by-2*length(confint)-by-p 3D array. Each third dimension refers to an element of beta:

1. betaINT[,,1] is associated with first element of beta;

2. ...;

3. betaINT[,,p] is associated with last element of beta.

The first two columns contain the lower and upper confidence limits associated with conflev(1). Columns three and four contain the lower and upper confidence limits associated with conflev(2); ...; The last two columns contain the lower and upper confidence limits associated with conflev(end). For example betaINT[,3:4,5] contain the lower and upper confidence limits for the fifth element of beta using confidence level specified in the second element of input option conflev.

sigma2INT

confidence interval for s2.

1. 1st col = fwd search index;

2. 2nd col = lower confidence limit based on conflev(1);

3. 3rd col = upper confidence limit based on conflev(1);

4. 4th col = lower confidence limit based on conflev(2);

5. 5th col = upper confidence limit based on conflev(2);

6. ...

7. penultimate col = lower confidence limit based on conflev(end);

8. last col = upper confidence limit based on conflev(end).

X

the data matrix X

y

the response vector y

The object has class "fsreda".

Examples

 ## Not run: 
    data(hbk, package="robustbase")
    (out <- fsreg(Y~., data=hbk, method="FS", monitoring=TRUE))
    class(out)
    summary(out)

## End(Not run)