317 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
Artritis séptica de rodilla por Pantoea agglomerans: caso clínico
Presentamos un caso clínico de artritis séptica de rodilla causado por Pantoea agglomerans, inoculado en la articulación mediante un pinchazo con cuerpo vegetal. Este bacilo gram (-) se ha asociado a la producción de artritis séptica en algunas ocasiones, pero nunca en nuestro país hasta la fecha y según nuestro conocimiento. Artritis originadas por punciones con vegetales y etiquetadas como asépticas, enmascaran en nuestra opinión verdaderos cuadros infecciosos. Como el tratamiento de cualquier artritis purulenta, deben combinarse el drenaje (en este caso mediante artroscopia) y antibioterapia, lo que en nuestro caso consiguió la curación del paciente.We report a case of septic arthritis of the knee
caused by Pantoea agglomerans, that gained access into
the joint by a puncture with a vegetal body. This gram –ve
bacillus has been occasionally linked to cases of septic
arthritis, but never in our country up to date and to our know-
ledge. We think that arthritis related to punctures with plants
and labelled as “aseptic”, mask in fact septic processes. As
in any pyogenic arthritis, adequate drainage of joint fluid
(through arthroscopy in this case) and antimicrobial therapy
must be used together; this approach allowed the healing of
our patient
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