394 research outputs found
The LIL for -statistics in Hilbert spaces
We give necessary and sufficient conditions for the (bounded) law of the
iterated logarithm for -statistics in Hilbert spaces. As a tool we also
develop moment and tail estimates for canonical Hilbert-space valued
-statistics of arbitrary order, which are of independent interest
Exponential and moment inequalities for U-statistics
A Bernstein-type exponential inequality for (generalized) canonical
U-statistics of order 2 is obtained and the Rosenthal and Hoffmann-J{\o}rgensen
inequalities for sums of independent random variables are extended to
(generalized) U-statistics of any order whose kernels are either nonnegative or
canonicalComment: 22 page
A Smirnov-Bickel-Rosenblatt theorem for compactly-supported wavelets
In nonparametric statistical problems, we wish to find an estimator of an
unknown function f. We can split its error into bias and variance terms;
Smirnov, Bickel and Rosenblatt have shown that, for a histogram or kernel
estimate, the supremum norm of the variance term is asymptotically distributed
as a Gumbel random variable. In the following, we prove a version of this
result for estimators using compactly-supported wavelets, a popular tool in
nonparametric statistics. Our result relies on an assumption on the nature of
the wavelet, which must be verified by provably-good numerical approximations.
We verify our assumption for Daubechies wavelets and symlets, with N = 6, ...,
20 vanishing moments; larger values of N, and other wavelet bases, are easily
checked, and we conjecture that our assumption holds also in those cases
Minimax Number of Strata for Online Stratified Sampling given Noisy Samples
We consider the problem of online stratified sampling for Monte Carlo integration of a function given a finite budget of noisy evaluations to the function. More precisely we focus on the problem of choosing the number of strata as a function of the budget . We provide asymptotic and finite-time results on how an oracle that has access to the function would choose the partition optimally. In addition we prove a \textit{lower bound} on the learning rate for the problem of stratified Monte-Carlo. As a result, we are able to state, by improving the bound on its performance, that algorithm MC-UCB, defined in~\citep{MC-UCB}, is minimax optimal both in terms of the number of samples n and the number of strata K, up to a . This enables to deduce a minimax optimal bound on the difference between the performance of the estimate outputted by MC-UCB, and the performance of the estimate outputted by the best oracle static strategy, on the class of Hölder continuous functions, and upt to a
Concentration Inequalities and Confidence Bands for Needlet Density Estimators on Compact Homogeneous Manifolds
Let be a random sample from some unknown probability density
defined on a compact homogeneous manifold of dimension . Consider a 'needlet frame' describing a localised
projection onto the space of eigenfunctions of the Laplace operator on with corresponding eigenvalues less than , as constructed in
\cite{GP10}. We prove non-asymptotic concentration inequalities for the uniform
deviations of the linear needlet density estimator obtained from an
empirical estimate of the needlet projection of . We apply these results to construct risk-adaptive
estimators and nonasymptotic confidence bands for the unknown density . The
confidence bands are adaptive over classes of differentiable and
H\"{older}-continuous functions on that attain their H\"{o}lder
exponents.Comment: Probability Theory and Related Fields, to appea
Analysis of the production of ethylene in 2,4-D resistant and sensitive biotypes of "Papaver rhoeas L."
Hasta el momento no se ha realizado ningún estudio en España a fin de indagar en los mecanismos de resistencia de “Papaver Rhoeas” al 2,4-D. En otros trabajos se ha demostrado como la producción de etileno está involucrada en la respuesta resistente de ciertas malas hierbas a auxinas sintéticas. En el presente estudio se ha observado que las plantas sensibles de amapola producen más etileno que las resistentes después de la aplicación de 2,4-D. Estos resultados podrían ayudar a comprender de mejor manera como ciertos biotipos son capaces de resistir a este producto.So far there has been none study in Spain to investigate the 2,4-D resistance mechanism of Papaver rhoeas. Other studies have shown how ethylene production is involved in the response of certain resistant weeds when they are sprayed with synthetic auxins. In the present study it was observed that sensitive corn poppy plants produce more ethylene than resistant one after 2,4-D application. These findings could help to understanding how certain biotypes are able to resist this product
The Pioneer anomaly and the holographic scenario
In this paper we discuss the recently obtained relation between the
Verlinde's holographic model and the first phenomenological Modified Newtonian
dynamics. This gives also a promising possible explanation to the Pioneer
anomaly.Comment: 5 pages, Accepted for publication in Astrophysics & Space Scienc
- …