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Title: Novel model-free estimation approaches of linear dimension reduction Authors:  Lukas Fertl - TU Vienna (Austria) [presenting]
Abstract: The purpose is to introduce a new way of estimating the dimension reduction matrix $B$ in the dimension reduction model $y=f(B' x) + \epsilon$, where $B$ is a $p \times d$ ($d < p$) unknown matrix of parameters and $\epsilon$ is a random error independent of $x$. The idea is based on considering the variance of $y$ conditional on $x$ being in the span of a direction vector $v$ as an estimating equation. This estimator falls in the class of semi-parametric methods, and we will denote it as conditional variance estimators. The performance of the estimator is competitive compared to currently used ones. Its main advantage is that it is more robust against a wide range of distributions for $x$ and nonlinear $f()$. Extensions to other estimation or testing problems will be also presented. Furthermore, it can also be used when the size of the sample is smaller than the number of covariates ($n < p$).