ABSTRACT
In this section we describe the second estimator of the central class — the Generalized Sliced Average Variance Estimator, or GSAVE, which is a generalization of SAVE in the linear SDR setting, introduced by Lee et al. (2013). It can recover a larger portion of the central subspace than GSIR, when the central subspace is not complete. It is based on what we call the heteroscedastic conditional covariance operator, which is a different operator than the conditional variance operator developed prior to Lee et al. (2013). Because the heteroscedastic conditional operator involves the conditional mean such as E[f(X)g(X)|Y], it is convenient to construct the estimator using the L 2 ( F n ) $ L _{\scriptscriptstyle 2}(F _{\scriptscriptstyle n}) $ https://s3-euw1-ap-pe-df-pch-content-public-p.s3.eu-west-1.amazonaws.com/9781315119427/09dc902b-e49a-45e8-84d8-98b5c97c1e74/content/inline-math14_1.tif"/> inner product, in a space that contains a constant. For this reason, the geometry used in this chapter is different from that used in Chapter 13.
