报告（一）：Unifying inference for linear regression with near-integrated variables

时间：2021年10月1日9:00-10:00

地点：腾讯会议681828077

报告摘要：In linear time series regression, for least square estimators, there is a discrepancy in the limiting distributions of stationary and nonstationary variables. This makes statistical inference difficult as it must be decided which distribution should be used prior to constructing interval estimates and conducting hypothesis tests. This motivates us to develop a multiple linear regression model with stationary and nonstationary state variables to reduce this difficulty and propose a unifying inference procedure for the coefficient estimates. To facilitate this unifying inference, we propose a weighted estimation technique. The asymptotic distributions of the proposed estimators are developed. However, the asymptotic variance cannot be estimated well due to erratic behavior of the residual-based variance estimate. A traditional bootstrap interval estimate does not work well either, because bootstrap sampling from the residuals in this nonstationary setting can be riddled with many large values. A random weighting bootstrap method is therefore proposed for constructing confidence regions of the coefficients of state variables. The proposed method works well (with time constant or time varying error variance) in our simulations and outperforms existing approaches. We employ an empirical data set to examine the predictability of asset returns to highlight the value of our methodology.

报告（二）：Unifying inference for semiparametric regression

时间：2021年10月1日10:00-11:00

地点：腾讯会议 681828077

报告摘要：In the literature, a discrepancy in the limiting distributions of least square estimators between the stationary and nonstationary cases exists in various regression models with different persistence level regressors. This hinders further statistical inference since one has to decide which distribution should be used next. In this paper, we develop a semiparametric partially linear regression model with stationary and nonstationary regressors to attenuate this difficulty, and propose a unifying inference procedure for the coefficients. To be specific, we propose a profile weighted estimation equation method that facilitates the unifying inference. The proposed method is applied to the predictive regressions of stock returns, and an empirical likelihood procedure is developed to test the predictability. It is shown that the Wilks theorem holds for the empirical likelihood ratio regardless of predictors being stationary or not, which provides a unifying method for constructing confidence regions of the coefficients of state variables. Simulations show that the proposed method works well and has favorable finite sample performance over some existing approaches. An empirical application examining the predictability of equity returns highlights the value of our methodology.

报告（三）：Variable selection in distributed sparse regression under memory constraints

时间：2021年10月1日11:00-12:00

地点：腾讯会议 681828077

报告摘要：This paper studies variable selection using the penalized likelihood method for distributed sparse regression with large sample size n under a limited memory constraint, where the memory of one machine can only store a subset of data. This is a much needed research problem to be solved in the big data era. A naive divide-and-conquer method solving this problem is to split the whole data into N parts and run each part on one of N machines, aggregate the results from all machines via averaging, and finally obtain the selected variables. However, it tends to select more noise variables, and the false discovery rate may not be well controlled. We improve it by a special designed weighted average in aggregation. Theoretically, we establish asymptotic properties of the resulting estimators for the likelihood model with a diverging number of parameters. Under some regularity conditions we establish oracle properties in the sense that our distributed estimator shares the same asymptotic efficiency as the estimator based on the full sample. Computationally, a distributed penalized likelihood algorithm is proposed to refine the results in the context of general likelihoods. Furthermore, the proposed method is evaluated by simulations and a real example.

报告人简介：蒋建成教授， University of North Carolina at Charlotte数学与统计系教授。主要从事生物统计、金融计量经济学、非参数统计、数据科学等方面的研究，在Annals of Statistics, Biometrika, Journal of American Statistical Association, Journal of the Royal Statistical Society 等国际著名统计期刊发表论文50余篇,担任Statistica Sinica 等杂志副主编。