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Can SIR be as popular as multiple linear regression? (English) Zbl 0897.62069
Summary: Despite its limitation in exploring nonlinear structures, multiple linear regression (MLR) still retains its popularity among the practitioners. This is mainly because of the several seemingly irreplaceable features of MLR that users are accustomed to, including: (i) it is easy to implement; (ii) it has a solid theoretical foundation; (iii) diagnostic tools are available for model checking; (iv) standard errors are available for significance assessment; (v) output is easy to interpret.
Whether such advantages can be maintained or not is an important issue in developing new nonlinear methods for high dimension regression. This issue is studied for one of the recently proposed methods, sliced inverse regression (SIR). We show how to enhance the SIR analysis so that these features can be maintained.

62J05 Linear regression; mixed models
62H99 Multivariate analysis
62J02 General nonlinear regression