Finite-sample properties of estimators for first and second order autoregressive processes

Statistical Inference for Stochastic Processes - The class of autoregressive (AR) processes is extensively used to model temporal dependence in observed time series. Such models are easily...     

2-fold and 3-fold mixing: why 3-dot-type counterexamples are impossible in one dimension

V.A. Rohlin asked in 1949 whether 2-fold mixing implies 3-fold mixing for a stationary process (ξ_i )_i2ℤ, and the question remains open today. In 1978, F. Ledrappier exhibited a counterexample to the 2-fold mixing implies 3-fold mixing problem, the socalled 3-dot system, but in the context of stationary random fields indexed by ℤ². In this work, we first present an attempt to adapt Ledrappier's construction to the onedimensional case, which finally leads to a stationary process which is 2-fold but not 3-fold mixing conditionally to the σ-algebra generated by some factor process. Then, using arguments coming from the theory of joinings, we will give some strong obstacles proving that Ledrappier's counterexample can not be fully adapted to one-dimensional stationary processes.     

Ion mobility studies of electronically excited states of atomic transition metal cations: Development of an ion mobility source for guided ion beam experiments

The design of an ion mobility source developed to couple to a guided ion beam tandem mass spectrometer is presented. In these exploratory studies, metal ions are created continuously by electron ionization of the volatile hexacarbonyls of the three group 6 transition metals. These ions are focused into a linear hexapole ion trap, which collects the ions and then creates high intensity pulses of ions, avoiding excessive ion losses resulting from the low duty cycle of pulsed operation. The ion pulses are injected into a six-ring drift cell filled with helium where ions having different electronic configurations can separate because they have different ion mobilities. Such separation is observed for chromium ions and compares favorably with the pioneering work of Kemper and Bowers (J. Phys. Chem.1991, 95, 5134). The results are then extended to Mo(+) and W(+), which also show efficient configuration separation. The source conditions needed for high intensities and good configuration separation are discussed in detail and suggestions for further improvements are also provided.     

Planar photonic crystal polarization splitter

The differential dispersion relation for the E and H modes (TM-like and TE-like, respectively) in planar photonic crystals is used to control the polarization-dependent propagation of light. E- and H-polarized beams were separated by 10 degrees after propagating through a 20-microm-long planar photonic crystal in the wavelength range from 1250 to 1300 nm. The plane-wave expansion calculation matches well with the experimental results. This result represents the first demonstration, to our knowledge, of a polarization splitter realized in a planar photonic crystal configuration in the near-infrared wavelength range operating solely in transmission mode.     

Fabrication of multipassband moiré resonators in fibers by the dual-phase-mask exposure method

We report on the fabrication of in-fiber moiré filters by dual exposure of a nondedicated chirped phase mask. This simple technique produces broadband filters whose structure depends only on an intermediate stretch between two identical UV exposures. We demonstrate moiré filters with as many as four narrow passbands within a 2-nm stopband.     

Graphene-based Q-switched pulsed fiber laser in a linear configuration

A pulsed laser system is realized with graphene employed as a Q-switch.The graphene is exfoliated from its solution using an optical deposition and the optical tweezer effect.A fiber ferrule that already has the graphene deposited on it is inserted into an erbium-ytterbium laser(EYL)system with linear cavity configuration.We successfully demonstrate a pulsed EYL with a pulse duration of approximately 5.9μs and a repetition rate of 20.0 kHz.     

Sub-nanometer metrology of chirped phase masks by optical Moiré

Optical Moiré fringe formation between a linear and chirped phase mask has been investigated theoretically and experimentally and used to determine the chirp rate. Period difference determination down to 0.4 nm is demonstrated using a 1080 nm period linear grating and a nominally 1 nm/mm chirped grating. Direct optical diffraction is also used to independently assess the chirp rate.     

INLA goes extreme: Bayesian tail regression for the estimation of high spatio-temporal quantiles

This work is motivated by the challenge organized for the 10th International Conference on Extreme-Value Analysis (EVA2017) to predict daily precipitation quantiles at the \(99.8\%\) level for each month at observed and unobserved locations. Our approach is based on a Bayesian generalized additive modeling framework that is designed to estimate complex trends in marginal extremes over space and time. First, we estimate a high non-stationary threshold using a gamma distribution for precipitation intensities that incorporates spatial and temporal random effects. Then, we use the Bernoulli and generalized Pareto (GP) distributions to model the rate and size of threshold exceedances, respectively, which we also assume to vary in space and time. The latent random effects are modeled additively using Gaussian process priors, which provide high flexibility and interpretability. We develop a penalized complexity (PC) prior specification for the tail index that shrinks the GP model towards the exponential distribution, thus preventing unrealistically heavy tails. Fast and accurate estimation of the posterior distributions is performed thanks to the integrated nested Laplace approximation (INLA). We illustrate this methodology by modeling the daily precipitation data provided by the EVA2017 challenge, which consist of observations from 40 stations in the Netherlands recorded during the period 1972–2016. Capitalizing on INLA’s fast computational capacity and powerful distributed computing resources, we conduct an extensive cross-validation study to select the model parameters that govern the smoothness of trends. Our results clearly outperform simple benchmarks and are comparable to the best-scoring approaches of the other teams.     

A Dynamic Mixture Model for Unsupervised Tail Estimation without Threshold Selection

Exceedances over high thresholds are often modeled by fitting a generalized Pareto distribution (GPD) on R⁺. It is difficult to select the threshold, above which the GPD assumption is enough solid and enough data is available for inference. We suggest a new dynamically weighted mixture model, where one term of the mixture is the GPD, and the other is a light-tailed density distribution. The weight function varies on R⁺ in such a way that for large values the GPD component is predominant and thus takes the role of threshold selection. The full data set is used for inference on the parameters present in the two component distributions and in the weight function. Maximum likelihood provides estimates with approximate standard deviations. Our approach has been successfully applied to simulated data and to the (previously studied) Danish fire loss data set. We compare the new dynamic mixture method to Dupuis' robust thresholding approach in peaks-over-threshold inference. We discuss robustness with respect to the choice of the light-tailed component and the form of the weight function. We present encouraging simulation results that indicate that the new approach can be useful in unsupervised tail estimation, especially in heavy tailed situations and for small percentiles.