Locally adaptive estimation methods with application to univariate time series

The paper offers a unified approach to the study of three locally adaptive estimation methods in the context of univariate time series from both theoretical and empirical points of view. A general procedure for the computation of critical values is given. The underlying model encompasses all distributions from the exponential family providing for great flexibility. The procedures are applied to simulated and real financial data distributed according to the Gaussian, volatility, Poisson, exponential and Bernoulli models. Numerical results exhibit a very reasonable performance of the methods.Comment: Submitted to the Electronic Journal of Statistics (http://www.i-journals.org/ejs/) by the Institute of Mathematical Statistics (http://www.imstat.org

Probabilistic Particle Flow Algorithm for High Occupancy Environment

Algorithms based on the particle flow approach are becoming increasingly utilized in collider experiments due to their superior jet energy and missing energy resolution compared to the traditional calorimeter-based measurements. Such methods have been shown to work well in environments with low occupancy of particles per unit of calorimeter granularity. However, at higher instantaneous luminosity or in detectors with coarse calorimeter segmentation, the overlaps of calorimeter energy deposits from charged and neutral particles significantly complicate particle energy reconstruction, reducing the overall energy resolution of the method. We present a technique designed to resolve overlapping energy depositions of spatially close particles using a statistically consistent probabilistic procedure. The technique is nearly free of ad-hoc corrections, improves energy resolution, and provides new important handles that can improve the sensitivity of physics analyses: the uncertainty of the jet energy on an event-by-event basis and the estimate of the probability of a given particle hypothesis for a given detector response. When applied to the reconstruction of hadronic jets produced in the decays of tau leptons using the CDF-II detector at Fermilab, the method has demonstrated reliable and robust performance.Comment: Accepted by Nuclear Instruments and Methods

A New Mass Reconstruction Technique for Resonances Decaying to di-tau

Accurate reconstruction of the mass of a resonance decaying to a pair of $\tau$ leptons is challenging because of the presence of multiple neutrinos from $\tau$ decays. The existing methods rely on either a partially reconstructed mass, which has a broad spectrum that reduces sensitivity, or the collinear approximation, which is applicable only to the relatively small fraction of events. We describe a new technique, which provides an accurate mass reconstruction of the original resonance and does not suffer from the limitations of the collinear approximation. The major improvement comes from replacing assumptions of the collinear approximation by a requirement that mutual orientations of the neutrinos and other decay products are consistent with the mass and decay kinematics of a $\tau$ lepton. This is achieved by minimizing a likelihood function defined in the kinematically allowed phase space region. In this paper we describe the technique and illustrate its performance using $Z/\gamma^{*}\to\tau\tau$ and $H\to\tau\tau$ events simulated with the realistic detector resolution. The method is also tested on a clean sample of data $Z/\gamma^{*}\to\tau\tau$ events collected by the CDF experiment at the Tevatron. We expect that this new technique will allow for a major improvement in searches for the Higgs boson at both the LHC and the Tevatron.Comment: added new section with CDF data results; submitted to Nucl. Instrum. Method