Correction: on page 245, line 2, "i=1,...,d" should be "i=1,...,p".
The main codes are ssir.r and lasso.r for R.
But you need dyn.load() an object file first which compiled two Fortran files: lasso.f (from Fu 1998) and Tiball.f (all.f from Tibshirani 1997). In Windows: Use Rcmd SHLIB lasso.f Tibsall.f or just download the lasso.dll below.

• ssir.r
• lasso.r
• Tibsall.f
• lasso.f
• lasso.dll

Many dimension reduction methods including SIR estimate a basis of the central space. For example, consider $y=x1/(1.5+x2)^2+0.2\epsilon$. Suppose SIR or SSIR obtains an estimate of a basis, say, $\hat{\eta}_1, \hat{\eta}_2$. Usually, $\hat{\eta}_1$ does not equal to $(1,0,...,0)^T$. Also SIR methods does not control the sign(+/-) and magnitude of the vectors. This is why the paper reports the absolute value of the correlation. Simulations in this paper is done using $h=6$ slices.

• For example 1, $\hat{\eta}$ has been multiplied with a constant to make the first element be $1$ in order to compare the mean squared error on equal footing.
• For example 2, $r_1$ is the multiple correlation between $x1$ and two estimated sufficient predictors $(\hat{\beta}_1^{T}X, \hat{\beta}_2^{T}X)$.

Last updated on Oct 18, 2006.