51 research outputs found
Quadratic optimal functional quantization of stochastic processes and numerical applications
In this paper, we present an overview of the recent developments of
functional quantization of stochastic processes, with an emphasis on the
quadratic case. Functional quantization is a way to approximate a process,
viewed as a Hilbert-valued random variable, using a nearest neighbour
projection on a finite codebook. A special emphasis is made on the
computational aspects and the numerical applications, in particular the pricing
of some path-dependent European options.Comment: 41 page
Convergence of multi-dimensional quantized 's
We quantize a multidimensional (in the Stratonovich sense) by solving
the related system of 's in which the -dimensional Brownian motion has
been replaced by the components of functional stationary quantizers. We make a
connection with rough path theory to show that the solutions of the quantized
solutions of the converge toward the solution of the . On our way to
this result we provide convergence rates of optimal quantizations toward the
Brownian motion for -H\" older distance, , in .Comment: 43 page
Detecting the direction of a signal on high-dimensional spheres: Non-null and Le Cam optimality results
We consider one of the most important problems in directional statistics,
namely the problem of testing the null hypothesis that the spike direction
of a Fisher-von Mises-Langevin distribution on the -dimensional
unit hypersphere is equal to a given direction . After a reduction
through invariance arguments, we derive local asymptotic normality (LAN)
results in a general high-dimensional framework where the dimension goes
to infinity at an arbitrary rate with the sample size , and where the
concentration behaves in a completely free way with , which
offers a spectrum of problems ranging from arbitrarily easy to arbitrarily
challenging ones. We identify various asymptotic regimes, depending on the
convergence/divergence properties of , that yield different
contiguity rates and different limiting experiments. In each regime, we derive
Le Cam optimal tests under specified and we compute, from the Le Cam
third lemma, asymptotic powers of the classical Watson test under contiguous
alternatives. We further establish LAN results with respect to both spike
direction and concentration, which allows us to discuss optimality also under
unspecified . To investigate the non-null behavior of the Watson test
outside the parametric framework above, we derive its local asymptotic powers
through martingale CLTs in the broader, semiparametric, model of rotationally
symmetric distributions. A Monte Carlo study shows that the finite-sample
behaviors of the various tests remarkably agree with our asymptotic results.Comment: 47 pages, 4 figure
Testing Gait with Ankle-Foot Orthoses in Children with Cerebral Palsy by Using Functional Mixed-Effects Analysis of Variance
Dr Morrissey is part funded by the NIHR/HEE Senior Clinical Lecturer scheme. Tis report presents independent research part-funded by the National Institute for Health Research (NIHR) CAT SCL-2013-04-00
Similarity of samples and trimming
We say that two probabilities are similar at level if they are contaminated versions (up to an fraction) of the same common probability. We show how this model is related to minimal distances between sets of trimmed probabilities. Empirical versions turn out to present an overfitting effect in the sense that trimming beyond the similarity level results in trimmed samples that are closer than expected to each other. We show how this can be combined with a bootstrap approach to assess similarity from two data samples
Letter to the editor
This letter shows how the main result contained in a paper recently appeared in the Journal of Multivariate Analysis was in fact a particular case of a more general theorem published three years before. © 2011 Elsevier Inc
Searching for a common pooling pattern among several samples
The grades of a Spanish university access exam involving 10 graders are analyzed. The interest focuses on finding the greatest group of graders showing similar grading patterns or, equivalently, on detecting if there are graders whose grades exhibit significant deviations from the pattern determined by the remaining graders. Due to differences in background of the involved students and graders, homogeneity is too strong to be considered as a realistic null model. Instead, the weaker similarity model, which seems to be more appropriate in this setting, is considered. To handle this problem, a statistical procedure designed to search for a hidden main pattern is developed. The procedure is based on the detection and deletion of the graders that are significantly non-similar to (the pooled mixture of) the others. This is performed through the use of a probability metric, a bootstrap approach and a stepwise search algorithm. Moreover, the procedure also allows one to identify which part of the grades of each grader makes her/him different from the others. © 2013 Elsevier B.V. All rights reserved
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