Title Estimation of the Effective Dimension Reduction (edr) Space
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چکیده
Description The library contains R-functions to estimate the effective dimension reduction space in multi-index regression models.
منابع مشابه
A new sliced inverse regression method for multivariate response
A semiparametric regression model of a q-dimensional multivariate response y on a p-dimensional covariate x is considered. A new approach is proposed based on sliced inverse regression (SIR) for estimating the effective dimension reduction (EDR) space without requiring a prespecified parametric model. The convergence at rate √ n of the estimated EDR space is shown. The choice of the dimension o...
متن کاملDetermining the dimension in Sliced
Sliced inverse regression and principal Hessian directions (Li, 1991, 1992) aim to reduce the dimensionality of regression problems. An important step in the method is the determination of a suitable dimension. While statistical tests based on the nullity eigenvalues are usually suggested, we here focus on the quality of the estimation of the eeective dimension reduction (edr) spaces. Essential...
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In this paper, we consider regression models with a Hilbert-space-valued predictor and a scalar response, where the response depends on the predictor only through a finite number of projections. The linear subspace spanned by these projections is called the effective dimension reduction (EDR) space. To determine the dimensionality of the EDR space, we focus on the leading principal component sc...
متن کاملSmoothed Functional Inverse Regression
A generalization of Sliced Inverse Regression to functional regressors was introduced by Ferré and Yao (2003). Here we first address the issue of the identifiability of the Effective Dimension Reduction (EDR) space. Next, we estimate the covariance operator of the conditional expectation by means of kernel estimates. Consistency is proved and this extends the results of Zhu and Fang (1996) in t...
متن کاملA New Algorithm for Estimating the Effective Dimension-Reduction Subspace
The statistical problem of estimating the effective dimension-reduction (EDR) subspace in the multi-index regression model with deterministic design and additive noise is considered. A new procedure for recovering the directions of the EDR subspace is proposed. Many methods for estimating the EDR subspace perform principal component analysis on a family of vectors, say β̂1, . . . , β̂L, nearly ly...
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