63 research outputs found
Adaptive circular deconvolution by model selection under unknown error distribution
We consider a circular deconvolution problem, in which the density of a
circular random variable must be estimated nonparametrically based on an
i.i.d. sample from a noisy observation of . The additive measurement
error is supposed to be independent of . The objective of this work was to
construct a fully data-driven estimation procedure when the error density
is unknown. We assume that in addition to the i.i.d. sample from ,
we have at our disposal an additional i.i.d. sample drawn independently from
the error distribution. We first develop a minimax theory in terms of both
sample sizes. We propose an orthogonal series estimator attaining the minimax
rates but requiring optimal choice of a dimension parameter depending on
certain characteristics of and , which are not known in practice.
The main issue addressed in this work is the adaptive choice of this dimension
parameter using a model selection approach. In a first step, we develop a
penalized minimum contrast estimator assuming that the error density is known.
We show that this partially adaptive estimator can attain the lower risk bound
up to a constant in both sample sizes and . Finally, by randomizing the
penalty and the collection of models, we modify the estimator such that it no
longer requires any previous knowledge of the error distribution. Even when
dispensing with any hypotheses on , this fully data-driven estimator
still preserves minimax optimality in almost the same cases as the partially
adaptive estimator. We illustrate our results by computing minimal rates under
classical smoothness assumptions.Comment: Published in at http://dx.doi.org/10.3150/12-BEJ422 the Bernoulli
(http://isi.cbs.nl/bernoulli/) by the International Statistical
Institute/Bernoulli Society (http://isi.cbs.nl/BS/bshome.htm
Consistent Density Deconvolution under Partially Known Error Distribution
We estimate the distribution of a real-valued random variable from contaminated observations. The additive error is supposed to be normally distributed, but with unknown variance. The distribution is identifiable from the observations if we restrict the class of considered distributions by a simple condition in the time domain. A minimum distance estimator is shown to be consistent imposing only a slightly stronger assumption than the identification condition.deconvolution, error measurement, density estimation
Adaptive Gaussian inverse regression with partially unknown operator
This work deals with the ill-posed inverse problem of reconstructing a
function given implicitly as the solution of , where is a
compact linear operator with unknown singular values and known eigenfunctions.
We observe the function and the singular values of the operator subject to
Gaussian white noise with respective noise levels and .
We develop a minimax theory in terms of both noise levels and propose an
orthogonal series estimator attaining the minimax rates. This estimator
requires the optimal choice of a dimension parameter depending on certain
characteristics of and . This work addresses the fully data-driven
choice of the dimension parameter combining model selection with Lepski's
method. We show that the fully data-driven estimator preserves minimax
optimality over a wide range of classes for and and noise levels
and . The results are illustrated considering Sobolev
spaces and mildly and severely ill-posed inverse problems
First second of leptons
A poorly constrained parameter in the Standard Model of Cosmology is the
lepton asymmetry l = \sum_f l_f=\sum_f(n_f+n_{\nu_f})/s. Each flavour asymmetry
l_f with f=e, \mu, {\tau} is the sum of the net particle density of the charged
leptons n_f and their corresponding neutrinos, normalized with the entropy
density s. Constraints on l_f \leq O(0.1) from BBN and CMB allow for lepton
flavour asymmetries orders of magnitudes larger then the baryon asymmetry b ~
10^{-10}. In this article we show how such large lepton (flavour) asymmetries
influence the early universe, in particular the freeze out of WIMPs and the
cosmic QCD transition.Comment: 4 pages, 2 figures; prepared for the 12th international conference on
Topics in Astroparticle and Underground Physics, TAUP2011. v2: matches
accepted versio
Nonparametric frontier estimation from noisy data
A new nonparametric estimator of production frontiers is defined and studied when the data set of production units is contaminated by measurement error. The measurement error is assumed to be an additive normal random variable on the input variable, but its variance is unknown. The estimator is a modification of the m-frontier, which necessitates the computation of a consistent estimator of the conditional survival function of the input variable given the output variable. In this paper, the identification and the consistency of a new estimator of the survival function is proved in the presence of additive noise with unknown variance. The performance of the estimator is also studied through simulated data.production frontier, deconvolution, measurement error, efficiency analysis
Nonparametric Frontier Estimation from Noisy Data
A new nonparametric estimator of production a frontier is defined and studied when the data set of production units is contaminated by measurement error. The measurement error is assumed to be an additive normal random variable on the input variable, but its variance is unknown. The estimator is a modification of the m-frontier, which necessitates the computation of a consistent estimator of the conditional survival function of the input variable given the output variable. In this paper, the identification and the consistency of a new estimator of the survival function is proved in the presence of additive noise with unknown variance. The performance of the estimator is also studied through simulated data.
Non parametric estimation in the presence of noise with unknown distribution
This thesis is concerned with the development of estimation techniques in four models involving statistical inverse problems with noise in the operator. Firstly, we consider a density deconvolution model on the real line: a probability density is to be estimated from observations which are subject to an independent additive measurement error. Assuming that the error is centered and normally distributed with unknown variance, we develop an intuitive time-domain condition on the target density which allows for its identification and consistent estimation by means of a minimum distance estimator. Next, we consider a stochastic frontier model. Our aim consists in estimating the support boundary of a two dimensional probability distribution based on observations with independent additive and normally distributed noise in one dimension. Exploiting the deconvolution techniques from the first chapter, we develop a consistent two step procedure for the non parametric estimation of the frontier, using in particular the m-frontier technique. In the following chapter, we look at the special density deconvolution model where the densities are supported on the circle instead of the real line. We drop the normality hypothesis for the error distribution. Instead, we assume that in addition to the sample of contaminated observations, a sample drawn from the error distribution is available. Minimax theory in both sample sizes is developed and a fully data-driven estimator is defined and shown to be minimax optimal over a wide range of density classes. Finally, we consider a regression model with instrumental variables. The minimax rates for the non parametric estimation of the structural function are developed and shown to be attained by an adaptive estimator in certain cases
Mapping Spikes to Sensations
Single-unit recordings conducted during perceptual decision-making tasks have yielded tremendous insights into the neural coding of sensory stimuli. In such experiments, detection or discrimination behavior (the psychometric data) is observed in parallel with spike trains in sensory neurons (the neurometric data). Frequently, candidate neural codes for information read-out are pitted against each other by transforming the neurometric data in some way and asking which code’s performance most closely approximates the psychometric performance. The code that matches the psychometric performance best is retained as a viable candidate and the others are rejected. In following this strategy, psychometric data is often considered to provide an unbiased measure of perceptual sensitivity. It is rarely acknowledged that psychometric data result from a complex interplay of sensory and non-sensory processes and that neglect of these processes may result in misestimating psychophysical sensitivity. This again may lead to erroneous conclusions regarding the adequacy of candidate neural codes. In this review, we first discuss requirements on the neural data for a subsequent neurometric-psychometric comparison. We then focus on different psychophysical tasks for the assessment of detection and discrimination performance and the cognitive processes that may underlie their execution. We discuss further factors that may compromise psychometric performance and how they can be detected or avoided. We believe that these considerations point to shortcomings in our understanding of the processes underlying perceptual decisions, and therefore offer potential for future research
Particle asymmetries in the early universe
The total lepton asymmetry in our universe is only poorly
constrained by theories and experiments. It might be orders of magnitudes
larger than the observed baryon asymmetry , . We found that the dynamics of the cosmic QCD transition
changes for large asymmetries. Predictions for asymmetries in a single flavour
allow even larger values. We find that asymmetries of in a single or two flavours change the relic abundance of WIMPs.
However, large lepton and large individual lepton flavour asymmetries
influences significantly the dynamics of the early universe.Comment: 7 pages,8 figures; Proceedings of the Erice workshop on Nuclear
Physics 2010 "Particle and Nuclear Astrophysics
Lepton asymmetry and the cosmic QCD transition
We study the influence of lepton asymmetry on the evolution of the early
Universe. The lepton asymmetry is poorly constrained by observations and
might be orders of magnitude larger than the baryon asymmetry , . We find that lepton asymmetries that are large compared to the
tiny baryon asymmetry, can influence the dynamics of the QCD phase transition
significantly. The cosmic trajectory in the phase diagram of strongly
interacting matter becomes a function of lepton (flavour) asymmetry. Large
lepton asymmetry could lead to a cosmic QCD phase transition of first order.Comment: 23 pages, 14 figures; matches published version, including Erratum.
Conclusions, pictures, numerics remained unchange
- …