Search results for " Statistics"
showing 10 items of 1891 documents
MODERATE DEVIATION PRINCIPLES FOR KERNEL ESTIMATOR OF INVARIANT DENSITY IN BIFURCATING MARKOV CHAINS MODELS
2021
Bitseki and Delmas (2021) have studied recently the central limit theorem for kernel estimator of invariant density in bifurcating Markov chains models. We complete their work by proving a moderate deviation principle for this estimator. Unlike the work of Bitseki and Gorgui (2021), it is interesting to see that the distinction of the two regimes disappears and that we are able to get moderate deviation principle for large values of the ergodic rate. It is also interesting and surprising to see that for moderate deviation principle, the ergodic rate begins to have an impact on the choice of the bandwidth for values smaller than in the context of central limit theorem studied by Bitseki and …
CENTRAL LIMIT THEOREM FOR KERNEL ESTIMATOR OF INVARIANT DENSITY IN BIFURCATING MARKOV CHAINS MODELS
2021
Bifurcating Markov chains (BMC) are Markov chains indexed by a full binary tree representing the evolution of a trait along a population where each individual has two children. Motivated by the functional estimation of the density of the invariant probability measure which appears as the asymptotic distribution of the trait, we prove the consistence and the Gaussian fluctuations for a kernel estimator of this density based on late generations. In this setting, it is interesting to note that the distinction of the three regimes on the ergodic rate identified in a previous work (for fluctuations of average over large generations) disappears. This result is a first step to go beyond the thresh…
CENTRAL LIMIT THEOREM FOR BIFURCATING MARKOV CHAINS
2020
Bifurcating Markov chains (BMC) are Markov chains indexed by a full binary tree representing the evolution of a trait along a population where each individual has two children. We first provide a central limit theorem for general additive functionals of BMC, and prove the existence of three regimes. This corresponds to a competition between the reproducing rate (each individual has two children) and the ergodicity rate for the evolution of the trait. This is in contrast with the work of Guyon (2007), where the considered additive functionals are sums of martingale increments, and only one regime appears. Our first result can be seen as a discrete time version, but with general trait evoluti…
Semiparametric models with functional responses in a survey sampling setting : model assisted estimation of electricity consumption curve
2010
International audience; Ce travail adopte une approche de type sondage quand le but est d'estimer une courbe moyenne d'une grande base de données de données fonctionnelles. Lorsque les capacités de stockage sont limitées, grâce aux techniques de sondage, une petite partie des observations est une alternative intéressante par rapport aux techniques de compression. Nous proposons ici de prendre en considération une information auxiliaire réelle ou multivariée obtenu à moindre coût sur la population toute entière, avec une approche semiparamétrique de type modèle assisté, dans le but d'améliorer les estimateurs d'Horvitz-Thompson de la courbe moyenne. D'abord, nous estimerons les composantes p…
Comment on the subdifferential formula given in the article "Algorithmic Analysis and Statistical Estimation of SLOPE via Approximate Message Passing"
2023
Subdifferential formula for the sorted 1 norm attracted lot of attention recently to derive screening procedures for SLOPE [5, 7], clustering and sparsity properties for SLOPE [1, 10] and explicit expressions for the proximal operator of the sorted 1 norm [4, 11]. In this note, we discuss the formula for the subdifferential of the sorted 1 norm given in the article of Bu et al., [3]. We believe that expressing the sorted 1 norm as the maximum of linear functions, as suggested by the authors, is an appropriate approach to derive its subdifferential. However the formula provided in this article contains many flaws and we hope that authors would take into account this note in order to rewrite …
The Solution Path of SLOPE
2023
The SLOPE estimator has the particularity of having null components (sparsity) and components that are equal in absolute value (clustering). The number of clusters depends on the regularization parameter of the estimator. This parameter can be chosen as a trade-off between interpretability (with a small number of clusters) and accuracy (with a small mean squared error or a small prediction error). Finding such a compromise requires to compute the solution path, that is the function mapping the regularization parameter to the estimator. We provide in this article an algorithm to compute the solution path of SLOPE.
Exploring the Solar Wind from Its Source on the Corona into the Inner Heliosphere during the First Solar Orbiter-Parker Solar Probe Quadrature
2021
This Letter addresses the first Solar Orbiter (SO) -- Parker Solar Probe (PSP) quadrature, occurring on January 18, 2021, to investigate the evolution of solar wind from the extended corona to the inner heliosphere. Assuming ballistic propagation, the same plasma volume observed remotely in corona at altitudes between 3.5 and 6.3 solar radii above the solar limb with the Metis coronagraph on SO can be tracked to PSP, orbiting at 0.1 au, thus allowing the local properties of the solar wind to be linked to the coronal source region from where it originated. Thanks to the close approach of PSP to the Sun and the simultaneous Metis observation of the solar corona, the flow-aligned magnetic fiel…
Tunable source of infrared pulses in gas-filled hollow core capillary
2020
International audience; We report a tunable source that generates pulses in the infrared from an optical parametric amplification in a gas-filled hollow core capillary based on four-wave mixing process, in which the phase matching strongly depends on the gas pressure and the pump. In our case, we have generated pulses from 1 to 1.6 m in the sub-µJ level together with a parametric amplification in the visible.
Fiber optical parametric polarizer
2013
In this work, a fiber-optical parametric polarizer (FOPP), i.e., a polarizing device based on parametric amplification in optical fibers is demonstrated. This was achieved for both the signal and idler waves with 25 dB gain over a broad bandwidth using the strong polarization-dependent gain (PDG) of parametric amplifiers. The experimental values of the degree of polarization (DOP) calculated from the Stokes parameters are indicated above each sphere. The gain spectra are also plotted with the parametric gain and the signal OSNR in insets. The Poincare sphere represents the three normalized Stokes parameters (S1,S2,S3) in unit radius. Results show that he DOP of the signal significantly incr…
Temporal coherence in mirrorless optical parametric oscillators
2012
International audience; One of the unique features of mirrorless optical parametric oscillators based on counterpropagating three-wave interactions is the narrow spectral width of the wave generated in the backward direction. In this work, we in- vestigate experimentally and numerically the influence that a strong phase modulation in the pump has on the spectral bandwidths of the parametric waves and on the efficiency of the nonlinear interaction. The effects of group-velocity mismatch and group-velocity dispersion are elucidated. In particular, it is shown that the substan- tial increase in temporal coherence of the backward-generated wave can be obtained even for pumping with a temporally…