Yannick Baraud

Testing convex hypotheses on the mean of a Gaussian vector. Application to testing qualitative hypotheses on a regression function

In this paper we propose a general methodology, based on multiple testing, for testing that the mean of a Gaussian vector in ℝn belongs to a convex set. We show that the test achieves its nominal level, and characterize a class of vectors over which the tests achieve a prescribed power. In the functional regression model this general methodology is applied to test some qualitative hypotheses on the regression function. For example, we test that the regression function is positive, increasing, convex, or more generally, satisfies a differential inequality. Uniform separation rates over classes of smooth functions are established and a comparison with other results in the literature is provided. A simulation study evaluates some of the procedures for testing monotonicity.

Confidence balls in Gaussian regression

Starting from the observation of an R^n-Gaussian vector of mean f and covariance matrix \\sigma^2 I_n (I_n is the identity matrix), we propose a method for building a Euclidean confidence ball around f, with prescribed probability of coverage. For each n, we describe its nonasymptotic property and show its optimality with respect to some criteria.

Estimator selection in the Gaussian setting

We consider the problem of estimating the mean

Estimating composite functions by model selection

f

A New Test of Linear Hypothesis in Regression

of a Gaussian vector

MODEL SELECTION FOR REGRESSION ON A RANDOM DESIGN

Y

Model selection for regression on a fixed design

with independent components of common unknown variance

Non-asymptotic minimax rates of testing in signal detection

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Adaptive tests of linear hypotheses by model selection

. Our estimation procedure is based on estimator selection. More precisely, we start with an arbitrary and possibly infinite collection

Adaptive estimation in autoregression or -mixing regression via model selection

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