arXiv subjects

Haoyu Wei

Publications and source records attributed to Haoyu Wei.

24 records · Page 2Linked to original sources

arXiv2022

Concentration inequalities of MLE and robust MLE

The Maximum Likelihood Estimator (MLE) serves an important role in statistics and machine learning. In this article, for i.i.d. variables, we obtain constant-specified and sharp concentration inequalities and oracle inequalities for the MLE only under exponential moment conditions. Furthermore, in a robust setting, the sub-Gaussian type oracle inequalities of the log-truncated maximum likelihood estimator are derived under the second-moment condition.

math.ST↗

arXiv2022

Sharper Sub-Weibull Concentrations

Constant-specified and exponential concentration inequalities play an essential role in the finite-sample theory of machine learning and high-dimensional statistics area. We obtain sharper and constants-specified concentration inequalities for the sum of independent sub-Weibull random variables, which leads to a mixture of two tails: sub-Gaussian for small deviations and sub-Weibull for large deviations from the mean. These bounds are new and improve existing bounds with sharper constants. In addition, a new sub-Weibull parameter if the italic should be retained. Please check the whole text. is also proposed, which enables recovering the tight concentration inequality for a random variable (vector). For statistical applications, we give an $\ell_2$-error of estimated coefficients in negative binomial regressions when the heavy-tailed covariates are sub-Weibull distributed with sparse structures, which is a new result for negative binomial regressions. In applying random matrices, we derive non-asymptotic versions of Bai-Yin's theorem for sub-Weibull entries with exponential tail bounds. Finally, by demonstrating a sub-Weibull confidence region for a log-truncated Z-estimator without the second-moment condition, we discuss and define the sub-Weibull type robust estimator for independent observations $\{X_i\}_{i=1}^{n}$ without exponential-moment conditions.

math.ST↗

arXiv2022

Heterogeneous Overdispersed Count Data Regressions via Double Penalized Estimations

This paper studies the non-asymptotic merits of the double $\ell_1$-regularized for heterogeneous overdispersed count data via negative binomial regressions. Under the restricted eigenvalue conditions, we prove the oracle inequalities for Lasso estimators of two partial regression coefficients for the first time, using concentration inequalities of empirical processes. Furthermore, derived from the oracle inequalities, the consistency and convergence rate for the estimators are the theoretical guarantees for further statistical inference. Finally, both simulations and a real data analysis demonstrate that the new methods are effective.

stat.ME↗

arXiv2021

Nonparametric Tests of Conditional Independence for Time Series

We propose consistent nonparametric tests of conditional independence for time series data. Our methods are motivated from the difference between joint conditional cumulative distribution function (CDF) and the product of conditional CDFs. The difference is transformed into a proper conditional moment restriction (CMR), which forms the basis for our testing procedure. Our test statistics are then constructed using the integrated moment restrictions that are equivalent to the CMR. We establish the asymptotic behavior of the test statistics under the null, the alternative, and the sequence of local alternatives converging to conditional independence at the parametric rate. Our tests are implemented with the assistance of a multiplier bootstrap. Monte Carlo simulations are conducted to evaluate the finite sample performance of the proposed tests. We apply our tests to examine the predictability of equity risk premium using variance risk premium for different horizons and find that there exist various degrees of nonlinear predictability at mid-run and long-run horizons.

econ.EM↗

arXiv2020

2-Step Sparse-View CT Reconstruction with a Domain-Specific Perceptual Network

Computed tomography is widely used to examine internal structures in a non-destructive manner. To obtain high-quality reconstructions, one typically has to acquire a densely sampled trajectory to avoid angular undersampling. However, many scenarios require a sparse-view measurement leading to streak-artifacts if unaccounted for. Current methods do not make full use of the domain-specific information, and hence fail to provide reliable reconstructions for highly undersampled data. We present a novel framework for sparse-view tomography by decoupling the reconstruction into two steps: First, we overcome its ill-posedness using a super-resolution network, SIN, trained on the sparse projections. The intermediate result allows for a closed-form tomographic reconstruction with preserved details and highly reduced streak-artifacts. Second, a refinement network, PRN, trained on the reconstructions reduces any remaining artifacts. We further propose a light-weight variant of the perceptual-loss that enhances domain-specific information, boosting restoration accuracy. Our experiments demonstrate an improvement over current solutions by 4 dB.

eess.IV↗

arXiv2020

Sparse Density Estimation with Measurement Errors

This paper aims to build an estimate of an unknown density of the data with measurement error as a linear combination of functions from a dictionary. Inspired by the penalization approach, we propose the weighted Elastic-net penalized minimal $\ell_2$-distance method for sparse coefficients estimation, where the adaptive weights come from sharp concentration inequalities. The optimal weighted tuning parameters are obtained by the first-order conditions holding with a high probability. Under local coherence or minimal eigenvalue assumptions, non-asymptotical oracle inequalities are derived. These theoretical results are transposed to obtain the support recovery with a high probability. Then, some numerical experiments for discrete and continuous distributions confirm the significant improvement obtained by our procedure when compared with other conventional approaches. Finally, the application is performed in a meteorology data set. It shows that our method has potency and superiority of detecting the shape of multi-mode density compared with other conventional approaches.

math.ST↗