Marie Chavent, Stéphane Girard, Vanessa Kuentz-Simonet, Benoit Liquet, Thi Mong Ngoc Nguyen and Jérôme Saracco 1 Institut de Mathématiques de Bordeaux, UMR CNRS 5251 Université de Bordeaux / Institut Polytechnique de Bordeaux, 351 cours de la libération, 33405 Talence Cedex, France e-mail: {marie.chavent,jerome.saracco}@math.u-bordeaux1.fr 2 Inria Bordeaux Sud-Ouest, CQFD team, France 3 Inria G...

The central subspace of a pair random variables $(y,\boldsymbol{x})\in \mathbb{R}^{p+1}$ is the minimal $\mathcal{S}$ such that $y\perp\!\!\!\!\!\perp \boldsymbol{x}|P_{\mathcal{S}}\boldsymbol{x}$. In this paper, we consider minimax rate estimating space under multiple index model $y=f(\boldsymbol{\beta }_{1}^{\tau }\boldsymbol{x},\boldsymbol{\beta }_{2}^{\tau }\boldsymbol{x},\ldots,\boldsymbol...

We develop tests of the hypothesis of no effect for selected predictors in regression, without assuming a model for the conditional distribution of the response given the predictors. Predictor effects need not be limited to the mean function and smoothing is not required. The general approach is based on sufficient dimension reduction, the idea being to replace the predictor vector with a lower...

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...

Existing model-free tests of the conditional coordinate hypothesis in sufficient dimension reduction (Cook (1998) [3]) focused mainly on the first-order estimation methods such as the sliced inverse regression estimation (Li (1991) [14]). Such testing procedures based on quadratic inference functions are difficult to be extended to second-order sufficient dimension reduction methods such as the...

Existing dimension reduction (DR) methods such as ordinary least squares (OLS) and sliced inverse regression (SIR) often perform poorly in the presence of outliers. Ellipsoidal trimming can be used to create outlier resistant DR methods that can also give useful results when the assumption of linearly related predictors is violated. Theory for SIR and OLS is reviewed, and it is shown that sever...

It is evidence that the demand for Asymmetric Digital Subscriber Line (ADSL) connections increases day by day in all European countries as much as worldwide and it is well known that Internet’s penetration is considerably amazing. At the same time, due to the fierce competition among ADSL connections providers, several packages are offered in attractive tariffs. As a product consists of various...

A regression model is best interpreted visually. Because we are limited to 2D displays, one way that we can fit a non-trivial model involving several predictor variables and still visually display it, is to partition the data and fit a simple model to each partition. We show how this can be achieved with a recursive partitioning algorithm called GUIDE. Further, we use examples to demonstrate ho...

A family of dimension-reduction methods, the inverse regression (IR) family, is developed by minimizing a quadratic objective function. An optimal member of this family, the inverse regression estimator (IRE), is proposed, along with inference methods and a computational algorithm. The IRE has at least three desirable properties: (1) Its estimated basis of the central dimension reduction subspa...