8,997 research outputs found
Stabilized Nearest Neighbor Classifier and Its Statistical Properties
The stability of statistical analysis is an important indicator for
reproducibility, which is one main principle of scientific method. It entails
that similar statistical conclusions can be reached based on independent
samples from the same underlying population. In this paper, we introduce a
general measure of classification instability (CIS) to quantify the sampling
variability of the prediction made by a classification method. Interestingly,
the asymptotic CIS of any weighted nearest neighbor classifier turns out to be
proportional to the Euclidean norm of its weight vector. Based on this concise
form, we propose a stabilized nearest neighbor (SNN) classifier, which
distinguishes itself from other nearest neighbor classifiers, by taking the
stability into consideration. In theory, we prove that SNN attains the minimax
optimal convergence rate in risk, and a sharp convergence rate in CIS. The
latter rate result is established for general plug-in classifiers under a
low-noise condition. Extensive simulated and real examples demonstrate that SNN
achieves a considerable improvement in CIS over existing nearest neighbor
classifiers, with comparable classification accuracy. We implement the
algorithm in a publicly available R package snn.Comment: 48 Pages, 11 Figures. To Appear in JASA--T&
Radio-to-TeV Phase-resolved Emission from the Crab Pulsar: The Annular Gap Model
In the framework of the three-dimensional (3D) annular gap model with
reasonable parameters (the magnetic inclination angle \alpha = 45 deg and the
view angle \zeta = 63 deg), we first use the latest hight energy data to
self-consistently calculate radio, X-ray, gamma-ray and TeV (MAGIC and VERITAS)
light curves, phase-averaged spectrum and phase-resolved spectra for the Crab
pulsar. It is found that the acceleration electric field and potential in the
annular gap and core gap are huge enough in the several tens of neutron star
radii. The pulsed emission of radio, X-ray, gamma-ray and TeV are mainly
generated from the emission of primary particles or secondary particles with
different emission mechanisms in the nearly similar region of the annular gap
located in the only one magnetic pole, which leads to the nearly
"phase-aligned" multi-wavelength light curves. The emission of peak 1 (P1) and
peak 2 (P2) is originated from the annular gap region near the null charge
surface, while the emission of bridge is mainly originated from the core gap
region. The phase-averaged spectrum and phase-resolved spectra of the Crab
pulsar from soft X-ray to TeV band are produced by four components: synchrotron
radiation from CR-induced and ICS-induced pairs dominates the X-ray band to
soft gamma-ray band (100 eV to 10 MeV); curvature radiation and synchrotron
radiation from the primary particles mainly contribute to gamma-ray band (10
MeV to \sim 20 GeV); ICS from the pairs significantly contributes to the TeV
gamma-ray band (\sim 20 GeV to 400 GeV). The multi-wavelength pulsed emission
from the Crab pulsar has been well modeled with the annular gap and core gap
model. To distinguish our single magnetic pole model from two-pole models, the
convincing values of the magnetic inclination angle and the viewing angle will
play a key role.Comment: 12 pages, 7 figures, 3 tables; published in ApJ on March 12. Due to
the character limitation, the abstract here has been adopted a shortened
versio
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