arXiv subjects

Zhixiang Zhang

Publications and source records attributed to Zhixiang Zhang.

27 records · Page 2Linked to original sources

arXiv2024

Robust Inference Under Heteroskedasticity via the Hadamard Estimator

Drawing statistical inferences from large datasets in a model-robust way is an important problem in statistics and data science. In this paper, we propose methods that are robust to large and unequal noise in different observational units (i.e., heteroskedasticity) for statistical inference in linear regression. We leverage the Hadamard estimator, which is unbiased for the variances of ordinary least-squares regression. This is in contrast to the popular White's sandwich estimator, which can be substantially biased in high dimensions. We propose to estimate the signal strength, noise level, signal-to-noise ratio, and mean squared error via the Hadamard estimator. We develop a new degrees of freedom adjustment that gives more accurate confidence intervals than variants of White's sandwich estimator. Moreover, we provide conditions ensuring the estimator is well-defined, by studying a new random matrix ensemble in which the entries of a random orthogonal projection matrix are squared. We also show approximate normality, using the second-order Poincare inequality. Our work provides improved statistical theory and methods for linear regression in high dimensions.

math.ST↗

arXiv2023

Wide binaries with white dwarf or neutron star companions discovered from Gaia DR3 and LAMOST

Gaia DR3 mission has identified and provided about 440,000 binary systems with orbital solutions, offering a valuable resource for searching binaries including a compact component. By combining the Gaia DR3 data with radial velocities (RVs) from the LAMOST spectroscopic survey, we identify three wide binaries possibly containing a compact object. For two of these sources with a main-sequence companion, no obvious excess is observed in the blue/red band of the Gaia DR3 XP spectra, and the LAMOST medium-resolution spectra exhibit clear single-lined features. The absence of an additional component from spectral disentangling analysis further suggests the presence of compact objects within these systems. On the other hand, the visible star of the third source is a stripped giant star. In contrast to most binaries including stripped stars, no emission line is detected in the optical spectra. The unseen star could potentially be a massive white dwarf or neutron star, but the possibility of an F-type dwarf star scenario cannot be ruled out. An examination of about ten binaries containing white dwarfs or neutron stars using both kinematic and chemical methods suggest most of these systems are located in the thin disk of the Milky Way.

astro-ph.SR↗

arXiv2023

Reconstructing high-order sequence features of dynamic functional connectivity networks based on diversified covert attention patterns for Alzheimer's disease classification

Recent studies have applied deep learning methods such as convolutional recurrent neural networks (CRNs) and Transformers to brain disease classification based on dynamic functional connectivity networks (dFCNs), such as Alzheimer's disease (AD), achieving better performance than traditional machine learning methods. However, in CRNs, the continuous convolution operations used to obtain high-order aggregation features may overlook the non-linear correlation between different brain regions due to the essence of convolution being the linear weighted sum of local elements. Inspired by modern neuroscience on the research of covert attention in the nervous system, we introduce the self-attention mechanism, a core module of Transformers, to model diversified covert attention patterns and apply these patterns to reconstruct high-order sequence features of dFCNs in order to learn complex dynamic changes in brain information flow. Therefore, we propose a novel CRN method based on diversified covert attention patterns, DCA-CRN, which combines the advantages of CRNs in capturing local spatio-temporal features and sequence change patterns, as well as Transformers in learning global and high-order correlation features. Experimental results on the ADNI and ADHD-200 datasets demonstrate the prediction performance and generalization ability of our proposed method.

eess.IV↗

arXiv2023

The disk reverberation mapping of X-ray weak quasars: a case study of SDSS J153913.47+395423.4

The widely adopted ``lamppost'' thermal reprocessing model, in which the variable UV/optical emission is a result of the accretion disk reprocessing of the highly fluctuating X-ray emission, can be tested by measuring inter-band time lags in quasars spanning a range of X-ray power. This work reports the inter-band time lag in an apparently X-ray weak quasar, SDSS J153913.47+395423.4. A significant cross-correlation with a time delay of $\sim 33$ days (observed-frame) is detected in the Zwicky Transient Facility (ZTF) $g$ and $r$ light curves of SDSS J153913.47+395423.4. The observed X-ray power seems to be too weak to account for the observed inter-band cross-correlation with time delay. Hence the X-ray weak quasar SDSS J153913.47+395423.4 is either intrinsically X-ray normal (but observationally X-ray weak), or the X-ray emission is not the only mechanism to drive UV/optical variability. In the former case, the required X-ray power is at least 19 times stronger than observed, which requires either an exceptionally anisotropic corona or Compton-thick obscuration. Alternatively, the Corona-heated Accretion disk Reprocessing (CHAR) or the EUV torus models may account for the observed time lags.

astro-ph.HE↗

arXiv2022

A White Dwarf-Main Sequence Binary Unveiled by Time-Domain Observations from LAMOST and TESS

We report a single-lined white dwarf-main sequence binary system, LAMOST J172900.17+652952.8, which is discovered by LAMOST's medium resolution time-domain surveys. The radial velocity semi-amplitude and orbital period of the optical visible star are measured by using the Palomar 200-inch telescope follow-up observations and the light curves from TESS. Thus the mass function of the invisible candidate white dwarf is derived, $f(M_{\rm{2}}) = 0.120\,\pm\,0.003\,M_{\odot}$. The mass of the visible star is measured based on the spectral energy distribution fitting, $M_{\mathrm{1}}$ = $0.81^{+0.07}_{-0.06}\,M_{\odot}$. Hence, the mass of its invisible companion is $M_{\rm{2}}\,\gtrsim\,0.63\,M_{\odot}$. The companion ought to be a compact object rather than a main-sequence star owing to the mass ratio $q = M_{\rm{2}} / M_{\rm 1} \gtrsim 0.78$ and the single-lined spectra. The compact object is likely to be a white dwarf except for small inclination angle, $i\,\lesssim\,40^{\circ}$. By using the GALEX NUV flux, the effective temperature of the white dwarf candidate is constrained as $T_{\rm eff}^{\rm WD}\,\lesssim\,12000-13500$ K. It is difficult to detect white dwarfs which are outshone by their bright companions via single-epoch optical spectroscopic surveys. Therefore, the optical time-domain surveys can play an important role in unveiling invisible white dwarfs and other compact objects in binaries.

astro-ph.SR↗

arXiv2021

Faint AGNs Favor Unexpectedly Long Inter-band Time Lags

Inconsistent conclusions are obtained from recent active galactic nuclei (AGNs) accretion disk inter-band time-lag measurements. While some works show that the measured time lags are significantly larger (by a factor of $\sim 3$) than the theoretical predictions of the Shakura \& Sunyaev disk (SSD) model, others find that the time-lag measurements are consistent with (or only slightly larger than) that of the SSD model. These conflicting observational results might be symptoms of our poor understanding of AGN accretion physics. Here we show that sources with larger-than-expected time lags tend to be less-luminous AGNs. Such a dependence is unexpected if the inter-band time lags are attributed to the light-travel-time delay of the illuminating variable X-ray photons to the static SSD. If, instead, the measured inter-band lags are related not only to the static SSD but also to the outer broad emission-line regions (BLRs; e.g., the blended broad emission lines and/or diffuse continua), our result indicates that the contribution of the non-disk BLR to the observed UV/optical continuum decreases with increasing luminosity ($L$), i.e., an anti-correlation resembling the well-known Baldwin effect. Alternatively, we argue that the observed dependence might be a result of coherent disk thermal fluctuations as the relevant thermal timescale, $τ_{\mathrm{TH}}\propto L^{0.5}$. With future accurate measurements of inter-band time lags, the above two scenarios can be distinguished by inspecting the dependence of inter-band time lags upon either the BLR components in the variable spectra or the timescales.

astro-ph.HE↗

arXiv2020

Tracy-Widom law for the extreme eigenvalues of large signal-plus-noise matrices

Let $\bY =\bR+\bX$ be an $M\times N$ matrix, where $\bR$ is a rectangular diagonal matrix and $\bX$ consists of $i.i.d.$ entries. This is a signal-plus-noise type model. Its signal matrix could be full rank, which is rarely studied in literature compared with the low rank cases. This paper is to study the extreme eigenvalues of $\bY\bY^*$. We show that under the high dimensional setting ($M/N\rightarrow c\in(0,1]$) and some regularity conditions on $\bR$ the rescaled extreme eigenvalue converges in distribution to Tracy-Widom distribution ($TW_1$).

math.ST↗

arXiv2020

Asymptotic independence of spiked eigenvalues and linear spectral statistics for large sample covariance matrices

We consider general high-dimensional spiked sample covariance models and show that their leading sample spiked eigenvalues and their linear spectral statistics are asymptotically independent when the sample size and dimension are proportional to each other. As a byproduct, we also establish the central limit theorem of the leading sample spiked eigenvalues by removing the block diagonal assumption on the population covariance matrix, which is commonly needed in the literature. Moreover, we propose consistent estimators of the $L_4$ norm of the spiked population eigenvectors. Based on these results, we develop a new statistic to test the equality of two spiked population covariance matrices. Numerical studies show that the new test procedure is more powerful than some existing methods.

math.ST↗

arXiv2014

Conditional Exact Law of Large Numbers and Asymmetric Information Economies with Aggregate Uncertainty

A stochastic model with a continuum of economic agents often involves shocks at both macro and micro levels. This can be formalized by a continuum of random variables that are conditionally independent given the macro level shocks. Based on the framework of a Fubini extension, the results on the exact law of large numbers and its converse for a con- tinuum of independent random variables in [14] are extended to the setting with conditional independence given general macro states. As an illustrative application, it is shown that any ex ante efficient allocation in an asymmetric information economy with general aggre- gate uncertainty has a (utility) equivalent allocation that is incentive compatible, which generalizes the corresponding results in [15] to the case with infinitely many states.

math.PR↗