科研成果 by Type: 期刊论文

2020
Huang, H., Gao, Y., Zhang, H., & Li, B. (2020). Weighted Lasso Estimates for Sparse Logistic Regressions: Non-asymptotic Properties with Measurement Error. Acta Mathematica Scientia.Abstract
When we are interested in high-dimensional system and focus on classification performance, the $\ell_{1}$-penalized logistic regression is becoming important and popular. However, the Lasso estimates could be problematic when penalties of different coefficients are all the same and not related to the data. We proposed two types of weighted Lasso estimates depending on covariates by the McDiarmid inequality. Given sample size $n$ and dimension of covariates $p$, the finite sample behavior of our proposed methods with a diverging number of predictors is illustrated by non-asymptotic oracle inequalities such as $\ell_{1}$-estimation error and squared prediction error of the unknown parameters. We compare the performance of our methods with former weighted estimates on simulated data, then apply these methods to do real data analysis.
Yu, J., Wang, H., Ai, M., & Zhang, H. (2020). Optimal Distributed Subsampling for Maximum Quasi-Likelihood Estimators with Massive Data. Journal of the American Statistical Association. 访问链接Abstract
Nonuniform subsampling methods are effective to reduce computational burden and maintain estimation efficiency for massive data. Existing methods mostly focus on subsampling with replacement due to its high computational efficiency. If the data volume is so large that nonuniform subsampling probabilities cannot be calculated all at once, then subsampling with replacement is infeasible to implement. This paper solves this problem using Poisson subsampling. We first derive optimal Poisson subsampling probabilities in the context of  quasi-likelihood estimation under the A- and L-optimality criteria. For a practically implementable algorithm with approximated optimal subsampling probabilities, we establish the consistency and asymptotic normality of the resultant estimators. To deal with the situation that the full data are stored in different blocks or at multiple locations, we develop a distributed subsampling framework, in which statistics are computed simultaneously on smaller partitions of the full data. Asymptotic properties of the resultant aggregated estimator are investigated. We illustrate and evaluate the proposed strategies through numerical experiments on simulated and real data sets.
Fan, Y., Zhang, H., & Yan, T. (2020). Asymptotic Theory for Differentially Private Generalized β-models with Parameters Increasing. Statistics and Its Interface, 13(3), 385 – 398. 访问链接
Ai, M., Yu, J., Zhang, H., & Wang, H. (2020). Optimal Subsampling for Big Data Regressions. Statistica Sinica. 访问链接
2019
Zhang, H., & Wu, X. (2019). Compound Poisson Point Processes, Concentration and Oracle Inequalities. Journal of Inequalities and Applications, 2019, 312. 访问链接Abstract
This note aims at presenting several new theoretical results for the compound Poisson point process, which follows the work of Zhang et al. (Insur. Math. Econ. 59:325–336, 2014). The first part provides a new characterization for a discrete compound Poisson point process (proposed by Aczél (Acta Math. Hung. 3(3):219–224, 1952)), it extends the characterization of the Poisson point process given by Copeland and Regan (Ann. Math. 37:357–362, 1936). Next, we derive some concentration inequalities for discrete compound Poisson point process (negative binomial random variable with unknown dispersion is a significant example). These concentration inequalities are potentially useful in count data regression. We give an application in the weighted Lasso penalized negative binomial regressions whose KKT conditions of penalized likelihood hold with high probability and then we derive non-asymptotic oracle inequalities for a weighted Lasso estimator.
2018
Zhang, H., Tan, K., & Bo, L. (2018). COM-negative binomial distribution: modeling overdispersion and ultrahigh zero-inflated count data. Frontiers of Mathematics in China, 13(4), 967–998. 访问链接Abstract
We focus on the COM-type negative binomial distribution with three parameters, which belongs to COM-type (ab, 0) class distributions and family of equilibrium distributions of arbitrary birth-death process. Besides, we show abundant distributional properties such as overdispersion and underdispersion, log-concavity, log-convexity (infinite divisibility), pseudo compound Poisson, stochastic ordering, and asymptotic approximation. Some characterizations including sum of equicorrelated geometrically distributed random variables, conditional distribution, limit distribution of COM-negative hypergeometric distribution, and Stein’s identity are given for theoretical properties. COM-negative binomial distribution was applied to overdispersion and ultrahigh zero-inflated data sets. With the aid of ratio regression, we employ maximum likelihood method to estimate the parameters and the goodness-of-fit are evaluated by the discrete Kolmogorov-Smirnov test.
2017
Zhang, H., & Jia, J. (2017). Elastic-net Regularized High-dimensional Negative Binomial Regression: Consistency and Weak Signals Detection. Working Paper. 访问链接
Zhang, H., Li, B., & Jay, K. G. (2017). A characterization of signed discrete infinitely divisible distributions. Studia Scientiarum Mathematicarum Hungarica, 54(4), 446–470. 访问链接
2015
刘庆,, 张慧铭,, & 李波,. (2015). 中国农业生产函数估计及农业投入产出研究. 统计与决策, (15), 127-130. 访问链接PKU 
2014
Zhang, H., Liu, Y., & Li, B. (2014). Notes on discrete compound Poisson model with applications to risk theory. Insurance: Mathematics and Economics, 56, 325-336. 访问链接