Marie-Luce Taupin

Adaptive density deconvolution with dependent inputs

In the convolution model Zi = Xi + εi, we give a model selection procedure to estimate the density of the unobserved variables (Xi)1≤i≤n, when the sequence (Xi)i≥1 is strictly stationary but not necessarily independent. This procedure depends on whether the density of the ɛi is supersmooth or ordinary smooth. The rates of convergence of the penalized contrast estimators are the same as in the independent framework, and are minimax over most regularity classes on ℝ. Our results apply to mixing sequences, but also to many other dependent sequences. When the errors are supersmooth, the condition on the dependence coefficients is the minimal condition of that type ensuring that the sequence (Xi)i≥1 is not a long-memory process.

Adaptive density estimation for general ARCH models

We consider a model Y null = σ null η null in which (σ null ) is not independent of the noise process (η null ) but σ null is independent of η null for each t . We assume that (σ null ) is stationary, and we propose an adaptive estimator of the density of ln(σ null 2 ) based on the observations Y null . Under a new dependence structure, the τ-dependency defined by Dedecker and Prieur (2005, Probability Theory and Related Fields 132, 203–236), we prove that the rates of this nonparametric estimator coincide with the rates obtained in the independent and identically distributed (i.i.d.) case when (σ null ) and (η null ) are independent. The results apply to various linear and nonlinear general autoregressive conditionally heteroskedastic (ARCH) processes. They are illustrated by simulations applying the deconvolution algorithm of Comte, Rozenholc, and Taupin (2006, Canadian Journal of Statistics 34, 431–452) to a new noise density.

Adaptive kernel estimation of the baseline function in the Cox model with high-dimensional covariates

We propose a novel kernel estimator of the baseline function in a general high-dimensional Cox model, for which we derive non-asymptotic rates of convergence. To construct our estimator, we first estimate the regression parameter in the Cox model via a LASSO procedure. We then plug this estimator into the classical kernel estimator of the baseline function, obtained by smoothing the so-called Breslow estimator of the cumulative baseline function. We propose and study an adaptive procedure for selecting the bandwidth, in the spirit of Goldenshluger and Lepski (2011). We state non-asymptotic oracle inequalities for the final estimator, which leads to a reduction in the rate of convergence when the dimension of the covariates grows.

Estimation in the nonlinear errors-in-variables model

Abstract In the nonlinear structural errors-in-variables model we propose a consistent estimator of the unknown parameter, using a modified least squares criterion. Its rate of convergence strongly related to the regularity of the regression function, is generally slower than the parametric rate of convergence n −1/2 . Nevertheless, it is of order (log n ) r /√ n , r > 0, for some analytic regression functions.

Sensitivity analysis of spatio-temporal models describing nitrogen transfers, transformations and losses at the landscape scale

Modelling complex systems such as agroecosystems often requires the quantification of a large number of input factors. Sensitivity analyses are useful to determine the appropriate spatial and temporal resolution of models and to reduce the number of factors to be measured or estimated accurately. Comprehensive spatial and temporal sensitivity analyses were applied to the NitroScape model, a deterministic spatially distributed model describing nitrogen transfers and transformations in rural landscapes. Simulations were led on a theoretical landscape that represented five years of intensive farm management and covering an area of

Comment on identification and estimation of nonlinear models using two samples with nonclassical measurement errors

3\, km^2

Penalized contrast estimator for adaptive density deconvolution

. Cluster analyses were applied to summarize the results of the sensitivity analysis on the ensemble of model outputs. The methodology we applied is useful to synthesize sensitivity analyses of models with multiple space-time input and output variables and could be ported to other models than NitroScape.

Semi-Parametric Estimation in the Nonlinear Structural Errors-in-Variables Model

A major challenge in statistics is to make inferences in the presence of measurement error or mismeasurement variables. Such mismeasurements appear in various contexts such as econometrics, biology or medicine. The paper by Carroll, Chen and Hu is completely in line with this challenging task. In this context, I would like to express my sincere and great appreciation for their contribution to this topic. It is a great pleasure for me to have the opportunity to contribute a discussion of this paper.