Displaying similar documents to “Estimation of the hazard function in a semiparametric model with covariate measurement error”

Model selection for regression on a random design

Yannick Baraud (2002)

ESAIM: Probability and Statistics

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We consider the problem of estimating an unknown regression function when the design is random with values in ℝ k . Our estimation procedure is based on model selection and does not rely on any prior information on the target function. We start with a collection of linear functional spaces and build, on a data selected space among this collection, the least-squares estimator. We study the performance of an estimator which is obtained by modifying this least-squares estimator on a set of...

Semiparametric deconvolution with unknown noise variance

Catherine Matias (2002)

ESAIM: Probability and Statistics

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This paper deals with semiparametric convolution models, where the noise sequence has a gaussian centered distribution, with unknown variance. Non-parametric convolution models are concerned with the case of an entirely known distribution for the noise sequence, and they have been widely studied in the past decade. The main property of those models is the following one: the more regular the distribution of the noise is, the worst the rate of convergence for the estimation of the signal’s...

Adaptive estimation of a quadratic functional of a density by model selection

Béatrice Laurent (2010)

ESAIM: Probability and Statistics

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We consider the problem of estimating the integral of the square of a density from the observation of a sample. Our method to estimate ∫ ℝ f 2 ( x ) d x is based on model selection some penalized criterion. We prove that our estimator achieves the adaptive rates established by Efroimovich and Low on classes of smooth functions. A key point of the proof is an exponential inequality for -statistics of order 2 due to Houdré and Reynaud.

Adaptive estimation of a quadratic functional of a density by model selection

Béatrice Laurent (2005)

ESAIM: Probability and Statistics

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We consider the problem of estimating the integral of the square of a density f from the observation of a n sample. Our method to estimate ∫ ℝ f 2 ( x ) d x is based on model selection via some penalized criterion. We prove that our estimator achieves the adaptive rates established by Efroimovich and Low on classes of smooth functions. A key point of the proof is an exponential inequality for U -statistics of order 2 due to Houdré and Reynaud.

Moderate deviations for two sample t-statistics

Hongyuan Cao (2007)

ESAIM: Probability and Statistics

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Let be a random sample from a population with mean and variance σ 1 2 , and be a random sample from another population with mean and variance σ 2 2 independent of {}. Consider the two sample t-statistic T = X ¯ - Y ¯ - ( μ 1 - μ 2 ) s 1 2 / n 1 + s 2 2 / n 2 . This paper shows that ln ²/2 for any satisfying → ∞, as provided 0 < < ∞. If, in addition, , , then P ( T ≥ x ) 1 - Φ ( x ) → 1 holds uniformly in