Exact adaptive pointwise estimation  on Sobolev classes of densities

Cristina Butucea

Displaying similar documents to “Exact adaptive pointwise estimation on Sobolev classes of densities”

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 $\int_{ℝ} f^{2} (x) d x$ 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.

On the minimizing point of the incorrectly centered empirical process and its limit distribution in nonregular experiments

Dietmar Ferger (2010)

ESAIM: Probability and Statistics

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Let be the empirical distribution function (df) pertaining to independent random variables with continuous df . We investigate the minimizing point ${\hat{τ}}_{n}$ of the empirical process , where is another df which differs from . If and are locally Hölder-continuous of order at a point our main result states that $n^{1 / α} ({\hat{τ}}_{n} - τ)$ converges in distribution. The limit variable is the almost sure unique minimizing point of a two-sided time-transformed homogeneous...

Towards parametrizing word equations

H. Abdulrab, P. Goralčík, G. S. Makanin (2010)

RAIRO - Theoretical Informatics and Applications

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Classically, in order to resolve an equation ≈ over a free monoid *, we reduce it by a suitable family $ℱ$ of substitutions to a family of equations ≈ , $f \in ℱ$ , each involving less variables than ≈ , and then combine solutions of ≈ into solutions of ≈ . The problem is to get $ℱ$ in a handy form. The method we propose consists in parametrizing the path traces in the so called associated to ≈ . We carry out such a parametrization in the case the prime equations in the graph involve at...