François Portier

Optimal transformation: A new approach for covering the central subspace

This paper studies a general family of methods for sufficient dimension reduction (SDR) called the test function (TF), based on the introduction of a nonlinear transformation of the response. By considering order 1 and 2 conditional moments of the predictors given the response, we distinguish two classes of methods. The optimal members of each class are calculated with respect to the asymptotic mean squared error between the central subspace (CS) and its estimate. Moreover the theoretical background of TF is developed under weaker conditions than the existing methods. Accordingly, simulations confirm that the resulting methods are highly accurate.

Integral approximation by kernel smoothing

Let

Efficiency and Bootstrap in the Promotion Time Cure Model

(X_1,\ldots,X_n)

On an extension of the promotion time cure model.

be an i.i.d. sequence of random variables in

Integral estimation based on Markovian design

\mathbb{R}^d

Rademacher complexity for Markov chains : Applications to kernel smoothing and Metropolis-Hasting

,

Parametric versus nonparametric: the fitness coefficient

d\geq 1

Asymptotic optimality of adaptive importance sampling.

. We show that, for any function

Efficiency of Z-estimators indexed by the objective functions

\varphi :\mathbb{R}^d\rightarrow\mathbb{R}

Continuous inverse regression

, under regularity conditions, \[n^ {1/2}\Biggl(n^{-1}\sum_{i=1}^n\frac{\varphi(X_i)}{\widehat{f}^(X_i)}- \int \varphi(x)\,dx\Biggr)\stackrel{\mathbb{P}}{\longrightarrow}0,\] where