Abstract: The asymptotic distribution of the test statistic for testing the dimensionality in the SIR-II method is derived and shown to be a linear combination of random variables under weak assumptions. This statistic is based on Li's (1991) sequential test statistic for sliced inverse regression (SIR). Also presented is a simulation study of the result.
Key words and phrases: Asymptotic distributions, Central subspaces, Dimension-reduction subspaces, Regression graphics.