Displaying similar documents to “Dynamics of an artificial slope”

Penalization versus Goldenshluger − Lepski strategies in warped bases regression

Gaëlle Chagny (2013)

ESAIM: Probability and Statistics

Similarity:

This paper deals with the problem of estimating a regression function , in a random design framework. We build and study two adaptive estimators based on model selection, applied with warped bases. We start with a collection of finite dimensional linear spaces, spanned by orthonormal bases. Instead of expanding directly the target function on these bases, we rather consider the expansion of  =  ∘ , where is the cumulative distribution function of the design, following...

Estimation in autoregressive model with measurement error

Jérôme Dedecker, Adeline Samson, Marie-Luce Taupin (2014)

ESAIM: Probability and Statistics

Similarity:

Consider an autoregressive model with measurement error: we observe = + , where the unobserved is a stationary solution of the autoregressive equation = ( ) + . The regression function is known up to a finite dimensional parameter to be estimated. The distributions of and are unknown and...

Goodness of fit test for isotonic regression

Cécile Durot, Anne-Sophie Tocquet (2010)

ESAIM: Probability and Statistics

Similarity:

We consider the problem of hypothesis testing within a monotone regression model. We propose a new test of the hypothesis : “” against the composite alternative : “” under the assumption that the true regression function is decreasing. The test statistic is based on the 𝕃 1 -distance between the isotonic estimator of and the function , since it is known that a properly centered and normalized version of this distance is asymptotically...

An ℓ1-oracle inequality for the Lasso in finite mixture gaussian regression models

Caroline Meynet (2013)

ESAIM: Probability and Statistics

Similarity:

We consider a finite mixture of Gaussian regression models for high-dimensional heterogeneous data where the number of covariates may be much larger than the sample size. We propose to estimate the unknown conditional mixture density by an -penalized maximum likelihood estimator. We shall provide an -oracle inequality satisfied by this Lasso estimator with the Kullback–Leibler loss. In particular, we give a condition on the regularization parameter of...

Model selection and estimation of a component in additive regression

Xavier Gendre (2014)

ESAIM: Probability and Statistics

Similarity:

Let  ∈ ℝ be a random vector with mean and covariance matrix where is some known  × -matrix. We construct a statistical procedure to estimate as well as under moment condition on or Gaussian hypothesis. Both cases are developed for known or unknown . Our approach is free from any prior assumption on and is based on non-asymptotic model selection methods....

Recursive bias estimation for multivariate regression smoothers

Pierre-André Cornillon, N. W. Hengartner, E. Matzner-Løber (2014)

ESAIM: Probability and Statistics

Similarity:

This paper presents a practical and simple fully nonparametric multivariate smoothing procedure that adapts to the underlying smoothness of the true regression function. Our estimator is easily computed by successive application of existing base smoothers (without the need of selecting an optimal smoothing parameter), such as thin-plate spline or kernel smoothers. The resulting smoother has better out of sample predictive capabilities than the underlying base smoother, or competing structurally...

Nonparametric regression estimation based on spatially inhomogeneous data: minimax global convergence rates and adaptivity

Anestis Antoniadis, Marianna Pensky, Theofanis Sapatinas (2014)

ESAIM: Probability and Statistics

Similarity:

We consider the nonparametric regression estimation problem of recovering an unknown response function on the basis of spatially inhomogeneous data when the design points follow a known density with a finite number of well-separated zeros. In particular, we consider two different cases: when has zeros of a polynomial order and when has zeros of an exponential order. These two cases correspond to moderate and severe data losses, respectively. We obtain asymptotic (as the sample size...

Towards a universally consistent estimator of the Minkowski content

Antonio Cuevas, Ricardo Fraiman, László Györfi (2013)

ESAIM: Probability and Statistics

Similarity:

We deal with a subject in the interplay between nonparametric statistics and geometric measure theory. The measure () of the boundary of a set  ⊂ ℝ (with  ≥ 2) can be formally defined, a simple limit, by the so-called Minkowski content. We study the estimation of () from a sample of random points inside and outside . The sample design assumes that, for each sample point, we know (without error) whether or not that point belongs to . Under this design we...

Algebraic Methods for Studying Interactions Between Epidemiological Variables

F. Ricceri, C. Fassino, G. Matullo, M. Roggero, M.-L. Torrente, P. Vineis, L. Terracini (2012)

Mathematical Modelling of Natural Phenomena

Similarity:

Background Independence models among variables is one of the most relevant topics in epidemiology, particularly in molecular epidemiology for the study of gene-gene and gene-environment interactions. They have been studied using three main kinds of analysis: regression analysis, data mining approaches and Bayesian model selection. Recently, methods of algebraic statistics have been...

Model selection for (auto-)regression with dependent data

Yannick Baraud, F. Comte, G. Viennet (2010)

ESAIM: Probability and Statistics

Similarity:

In this paper, we study the problem of non parametric estimation of an unknown regression function from dependent data with sub-Gaussian errors. As a particular case, we handle the autoregressive framework. For this purpose, we consider a collection of finite dimensional linear spaces ( linear spaces spanned by wavelets or piecewise polynomials on a possibly irregular grid) and we estimate the regression function by a least-squares estimator built on a data driven selected linear space...