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Ting Yan

Publications and source records attributed to Ting Yan.

45 records · Page 3Linked to original sources
arXiv2016

Asymptotics in directed exponential random graph models with an increasing bi-degree sequence

Although asymptotic analyses of undirected network models based on degree sequences have started to appear in recent literature, it remains an open problem to study statistical properties of directed network models. In this paper, we provide for the first time a rigorous analysis of directed exponential random graph models using the in-degrees and out-degrees as sufficient statistics with binary as well as continuous weighted edges. We establish the uniform consistency and the asymptotic normality for the maximum likelihood estimate, when the number of parameters grows and only one realized observation of the graph is available. One key technique in the proofs is to approximate the inverse of the Fisher information matrix using a simple matrix with high accuracy. Numerical studies confirm our theoretical findings.

math.ST↗
arXiv2015

Invisible Active Galactic Nuclei. II Radio Morphologies & Five New HI 21 cm Absorption Line Detections

We have selected a sample of 80 candidates for obscured radio-loud active galactic nuclei and presented their basic optical/near-infrared (NIR) properties in Paper 1. In this paper, we present both high-resolution radio continuum images for all of these sources and HI 21cm absorption spectroscopy for a few selected sources in this sample. A-configuration 4.9 and 8.5 GHz VLA continuum observations find that 52 sources are compact or have substantial compact components with size <0.5" and flux density >0.1 Jy at 4.9 GHz. The most compact 36 sources were then observed with the VLBA at 1.4 GHz. One definite and 10 candidate Compact Symmetric Objects (CSOs) are newly identified, a detection rate of CSOs ~3 times higher than the detection rate previously found in purely flux-limited samples. Based on possessing compact components with high flux densities, 60 of these sources are good candidates for absorption-line searches. Twenty seven sources were observed for HI 21cm absorption at their photometric or spectroscopic redshifts with only 6 detections made (one detection is tentative). However, five of these were from a small subset of six CSOs with pure galaxy optical/NIR spectra and for which accurate spectroscopic redshifts place the redshifted 21cm line in a RFI-free spectral window. It is likely that the presence of ubiquitous RFI and the absence of accurate spectroscopic redshifts preclude HI detections in similar sources (only one detection out of the remaining 22 sources observed, 14 of which have only photometric redshifts). Future searches for highly-redshifted HI and molecular absorption can easily find more distant CSOs among bright, blank field' radio sources but will be severely hampered by an inability to determine accurate spectroscopic redshifts for them due to their lack of rest-frame UV continuum.

astro-ph.GA↗
arXiv2014

Ranking in the generalized Bradley-Terry models when the strong connection condition fails

For nonbalanced paired comparisons, a wide variety of ranking methods have been proposed. One of the best popular methods is the Bradley-Terry model in which the ranking of a set of objects is decided by the maximum likelihood estimates (MLEs) of merits parameters. However, the existence of MLE for the Bradley-Terry model and its generalized models to allow for tied observation or home-field advantage or both to occur, crucially depends on the strong connection condition on the directed graph constructed by a win-loss matrix. When this condition fails, the MLE does not exist and hence there is no solution of ranking. In this paper, we propose an improved version of the $\varepsilon$ singular perturbation proposed by Conner and Grant (2000), to address this problem and extend it to the generalized Bradley-Terry models. Some necessary and sufficient conditions for the existence and uniqueness of the penalized MLEs for these generalized Bradley-Terry-$\varepsilon$ models are derived. Numerical studies show that the ranking is robust to the different $\varepsilon$. We apply the proposed methods to the data of the 2008 NFL regular season.

stat.ME↗
arXiv2014

Approximating the inverse of a balanced symmetric matrix with positive elements

For an $n\times n$ balanced symmetric matrix $T=(t_{i,j})$ with positive elements satisfying $t_{i,i}= \sum_{j\neq i} t_{i,j}$ and certain bounding conditions, we propose to use the matrix $S=(s_{i,j})$ to approximate its inverse, where $s_{i,j}=δ_{i,j}/t_{i,i}-1/t_{..}$, $δ_{i,j}$ is the Kronecker delta function, and $t_{..}=\sum_{i,j=1 }^{n}(1-δ_{i,j}) t_{i,j}$. An explicit bound on the approximation error is obtained, showing that the inverse is well approximated to order $1/(n-1)^2$ uniformly.

math.ST↗
arXiv2014

Asymptotic normality in the maximum entropy models on graphs with an increasing number of parameters

Maximum entropy models, motivated by applications in neuron science, are natural generalizations of the $β$-model to weighted graphs. Similar to the $β$-model, each vertex in maximum entropy models is assigned a potential parameter, and the degree sequence is the natural sufficient statistic. Hillar and Wibisono (2013) has proved the consistency of the maximum likelihood estimators. In this paper, we further establish the asymptotic normality for any finite number of the maximum likelihood estimators in the maximum entropy models with three types of edge weights, when the total number of parameters goes to infinity. Simulation studies are provided to illustrate the asymptotic results.

math.ST↗
arXiv2012

Grouped sparse paired comparisons in the Bradley-Terry model

In a wide class of paired comparisons, especially in the sports games, in which all subjects are divided into several groups, the intragroup comparisons are dense and the intergroup comparisons are sparse. Typical examples include the NFL regular season. Motivated by these situations, we propose group sparsity for paired comparisons and show the consistency and asymptotical normality of the maximum likelihood estimate in the Bradley-Terry model when the number of parameters goes to infinity in this paper. Simulations are carried out to illustrate the group sparsity and asymptotical results.

stat.OT↗
arXiv2012

The influence of fallback discs on the spectral and timing properties of neutron stars

Fallback discs around neutron stars (NSs) are believed to be an expected outcome of supernova explosions. Here we investigate the consequences of such a common outcome for the timing and spectral properties of the associated NS population, using Monte Carlo population synthesis models. We find that the long-term torque exerted by the fallback disc can substantially influence the late-time period distribution, but with quantitative differences which depend on whether the initial spin distribution is dominated by slow or fast pulsars. For the latter, a single-peaked initial spin distribution becomes bimodal at later times. Timing ages tend to underestimate the real age of older pulsars, and overestimate the age of younger ones. Braking indices cluster in the range 1.5 <~ n <~ 3 for slow-born pulsars, and -0.5 <~ n <~ 5 for fast-born pulsars, with the younger objects found predominantly below n <~ 3. Large values of n, while not common, are possible, and associated with torque transitions in the NS+disc system. The 0.1-10 keV thermal luminosity of the NS+disc system is found to be generally dominated by the disc emission at early times, t <~ 10^3 yr, but this declines faster than the thermal surface emission of the NS. Depending on the initial parameters, there can be occasional periods in which some NSs switch from the propeller to the accretion phase, increasing their luminosity up to the Eddington limit for ~ 10^3-10^4 years.

astro-ph.HE↗
arXiv2007

A two component jet model for the X-ray afterglow flat segment in short GRB 051221A

In the double neutron star merger or neutron star-black hole merger model for short GRBs, the outflow launched might be mildly magnetized and neutron rich. The magnetized neutron-rich outflow will be accelerated by the magnetic and thermal pressure and may form a two component jet finally, as suggested by Vlahakis, Peng & Königl (2003). We show in this work that such a two component jet model could well reproduce the multi-wavelength afterglow lightcurves, in particular the X-ray flat segment, of short GRB 051221A. In this model, the central engine need not to be active much longer than the prompt $γ-$ray emission.

astro-ph↗