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Variable Selection for Fixed Effects Varying Coefficient Models

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Acta Mathematica Sinica,English Series 2015年第1期31卷 91-110页

作者： Gao Rong LI heng lian Peng LAI heng PENG Beijing Center for Scientific and Engineering Computing College of Applied SciencesBeijing University of Technology School of Mathematics and Statistics The University of New South Wales School of Mathematics & Statistics Nanjing University of Information Science & Technology Department of Mathematics Hong Kong Baptist University

We consider the problem of variable selection for the fixed effects varying coefficient models. A variable selection procedure is developed using basis function approximations and group nonconcave penalized functions, and the fixed effects are removed using the proper weight matrices. The proposed procedure simultaneously removes the fixed individual effects, selects the significant variables and estimates the nonzero coefficient functions. With appropriate selection of the tuning parameters, an asymptotic theory for the resulting estimates is established under suitable conditions. Simulation studies are carried out to assess the performance of our proposed method, and a real data set is analyzed for further illustration.

关键词： Varying coefficient model fixed effect variable selection basis function

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Science China Mathematics 2024年第2期67卷 405-430页

作者： Junzhuo Gao Lei Wang heng lian School of Statistics and Data Science&LPMC Nankai UniversityTianjin 300071China Department of Mathematics City University of Hong KongHong KongChina

In this paper, we consider the unified optimal subsampling estimation and inference on the lowdimensional parameter of main interest in the presence of the nuisance parameter for low/high-dimensionalgeneralized linear models (GLMs) with massive data. We first present a general subsampling decorrelated scorefunction to reduce the influence of the less accurate nuisance parameter estimation with the slow convergencerate. The consistency and asymptotic normality of the resultant subsample estimator from a general decorrelatedscore subsampling algorithm are established, and two optimal subsampling probabilities are derived under theA- and L-optimality criteria to downsize the data volume and reduce the computational burden. The proposedoptimal subsampling probabilities provably improve the asymptotic efficiency of the subsampling schemes in thelow-dimensional GLMs and perform better than the uniform subsampling scheme in the high-dimensional GLMs.A two-step algorithm is further proposed to implement, and the asymptotic properties of the correspondingestimators are also given. Simulations show satisfactory performance of the proposed estimators, and twoapplications to census income and Fashion-MNIST datasets also demonstrate its practical applicability.

关键词： A-optimality decorrelated score subsampling high-dimensional inference L-optimality massive data

Upper bound solution of supporting pressure for a shallow square tunnel based on the Hoek-Brown failure criterion

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Journal of Zhejiang University-Science A(Applied Physics & Engineering) 2012年第4期13卷 284-292页

作者： Fu HUANG Xiao-li YANG lian-heng ZHAO School of Civil Engineering Central South UniversityChangsha 410075China

To analyze the stability of a shallow square tunnel, a new curved failure mechanism, representing the mechanical characteristics and collapsing form of this type of tunnel, is constructed. Based on the upper bound theorem of limit analysis and the Hoek-Brown nonlinear failure criterion, the supporting pressure derived from the virtual work rate equation is regarded as an objective function to achieve optimal calculation. By employing variational calculation to optimize the objective function, an upper bound solution for the supporting pressure and the collapsing block shape of a shallow square tunnel are obtained. To evaluate the validity of the failure mechanism proposed in this paper, the solutions computed by the curved failure mechanism are compared with the results calculated by the linear multiple blocks failure mechanism when the Hoek-Brown nonlinear failure criterion is converted into the Mohr-Coulomb linear criterion. The influences of rock mass parameters on the supporting pressure and collapsing block shape are discussed.

关键词： Shallow square tunnel Variational calculation Curved failure mechanism Supporting pressure Shape of collapsingblock Upper bound theorem

Discussion of the paper‘A review of distributed statistical inference’

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Statistical Theory and Related Fields 2022年第2期6卷 100-101页

作者： heng lian Department of Mathematics City University of Hong KongHong KongPeople’s Republic of China

The authors should be congratulated on their timely contribution to this emerging field with a compre-hensive review,which will certainly attract more researchers into this *** the simplest one-shot approach,the entire dataset is distributed on multiple machines,and each machine computes a local estimate based on local data only,and a central machine per-forms an aggregation calculation as a final processing *** more complicated settings,multiple communi-cations are carried out,typically passing also first-order information(gradient)and/or second-order informa-tion(Hession matrix)between local machines and the central *** review clearly separates the exist-ing works in this area into several sections,considering parameter regression,nonparametric regression,and other models including principal component analysis and variable screening.

关键词： local typically aggregation

Limit equilibrium method(LEM) of slope stability and calculation of comprehensive factor of safety with double strength-reduction technique

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Journal of Mountain Science 2017年第11期14卷 2311-2324页

作者： DENG Dong-ping LI liang ZHAO lian-heng School of Civil Engineering Central South University

When the slope is in critical limit equilibrium(LE) state, the strength parameters have different contribution to each other on maintaining slope stability. That is to say that the strength parameters are not simultaneously reduced. Hence, the LE stress method is established to analyze the slope stability by employing the double strengthreduction(DSR) technique in this work. For calculation model of slope stability under the DSR technique, the general nonlinear Mohr–Coulomb(M–C) criterion is used to describe the shear failure of slope. Meanwhile, the average and polar diameter methods via the DSR technique are both adopted to calculate the comprehensive factor of safety(FOS) of slope. To extend the application of the polar diameter method, the original method is improved in the proposed method. After comparison and analysis on some slope examples, the proposed method's feasibility is verified. Thereafter, the stability charts of slope suitable for engineering application are drawn. Moreover, the studies show that:(1) the average method yields similar results as that of the polardiameter method;(2) compared with the traditional uniform strength-reduction(USR) technique, the slope stability obtained using the DSR techniquetends to be more unsafe; and(3) for a slope in the critical LE state, the strength parameter φ, i.e., internal friction angle, has greater contribution on the slope stability than the strength parameters c, i.e., cohesion.

关键词： Slope stability Nonlinear Mohr-Coulomb (M-C) criterion Double strength-reduction(DSR) technique Slope Comprehensive Factor ofSafety (FOS) Stability charts

Limit equilibrium stability analysis of slopes under external loads

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Journal of Central South University 2016年第9期23卷 2382-2396页

作者： DENG Dong-ping ZHAO lian-heng LI liang School of Civil Engineering Central South University Changsha 410075 China

Two calculation modes for the effect of external load on slope stability, i.e., mode I in which the external load is thought to act on slope surface, and mode II in which the external load is thought to act on slip surface along the force action line, were considered. Meanwhile, four basic distribution patterns of external load were used, of which complex external loads could be composed. In analysis process, several limit equilibrium methods, such as Swedish method, simplified Bishop method, simplified Janbu method, Spencer method, Morgenstern-Price(M-P) method, Sarma method, and unbalanced thrust method, were also adopted to contrast their differences in slope stability under the external load. According to parametric analysis, some conclusions can be obtained as follows:(1) The external load, with the large magnitude, small inclination angle, and acting position close to the slope toe,has more positive effect on slope stability;(2) The results calculated using modes I and II of external load are similar, indicating that the calculation mode of external load has little influence on slope stability;(3) If different patterns of external loads are equivalent to each other, their slope stability under these external loads are the same, and if not, the external load leads to the better slope stability,as action position of the resultant force for external load is closer to the lower sliding point of slip surface.

关键词： slope stability calculation mode of external load distribution pattern of external load limit equilibrium slip surface factor of safety (FOS)

Limit equilibrium analysis for stability of soil nailed slope and optimum design of soil nailing parameters

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Journal of Central South University 2017年第11期24卷 2496-2503页

作者： DENG Dong-ping LI liang ZHAO lian-heng School of Civil Engineering Central South UniversityChangsha 410075China

Reinforcement of slopes using soil nailing can effectively improve slope stability, and it has been widely used in upgrading cut slopes. Based on the assumptions of stresses on the slip surface, a new method for analyzing the stability of a slope reinforced with soil nails was established in the limit equilibrium theory framework, by considering that slope sliding occurs owing to shear failure of the slip surface, which subjects to Mohr–Coulomb(M–C) strength criterion. Meanwhile, in order to easily analyze the stability of a soil nailed slope in actual engineering and facilitate optimum design of parameters for soil nailing, factor of safety(FOS) contour curve charts were drawn on the basis of the established linear proportional relationship between the spacing of soil nails and slope height, and the length of soil nails and slope height. Then, by analyzing and verifying the results obtained from classic examples, some conclusions can be got as follows: 1) The results obtained from the current method are close to those obtained from the traditional limit equilibrium methods, and the current method can provide a strict solution for the slope FOS as it satisfies all the static equilibrium conditions of a sliding body, thus confirming the feasibility of the current method; 2) The slope FOS contour curve charts can be used not only to reliably analyze the stability of a soil nailed slope, but also to design optimally the parameters of soil nailing for the slope with a certain safety requirement.

关键词： slope stability soil nailing limit equilibrium factor of safety contour curve optimum design

Influence of non-dimensional strength parameters on the seismic stability of cracked slopes

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Journal of Mountain Science 2019年第1期16卷 153-167页

作者： ZHAO lian-heng Cheng Xiao LI De-jian ZHANG Ying-bin School of Civil Engineering Central South University Key Laboratory of Heavy-haul Railway Engineering Structure Ministry of Education Central South University Key Laboratory of Transportation Tunnel Engineering Ministry of Education Southwest Jiaotong University Department of Geotechnical Engineering School of Civil Engineering Southwest Jiaotong University

Cracks in rock or soil slopes influence the stability and durability of the slopes. Seismic forces can trigger slope disasters, particularly in the cracked slopes. Considering the nonlinear characteristics of materials, the more generalized nonlinear failure criterion proposed by Baker is adopted. The influence of non-dimensional strength parameters on the stability of cracked slopes under earthquakes is performed using the upper bound limit analysis. The seismic displacement is calculated by adopting the logarithmic spiral failure surface according to the sliding rigid block model. Based on the existing studies, two methods for the stability analysis of cracked slopes under earthquakes are introduced: the pseudo-static method(with the factor of safety(Fs) as an evaluation index), and the displacement-based method(with the seismic displacement as an evaluation index). The pseudo-static method can only determine the instantaneous stability state of the cracked slope, yet the displacement-based methodreflects the stability variation of cracked slopes during earthquakes. The results indicate that the nondimensional strength parameters affect the factor of safety and seismic displacement of slopes significantly. The non-dimensional strength parameter(n) controlling the curvature of strength function shapes on the slope stability is affected by other parameters. Owing to cracks, the effect of non-dimensional strength parameters on seismic displacement becomes more significant.

关键词： Cracked slopes Upper bound limit analysis(UBLA) Generalized nonlinear failure criterion Pseudo-static method Displacement-based method

A general framework for frequentist model averaging In Celebration of Professor Lincheng Zhao's 75th Birthday

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Science China Mathematics 2019年第2期62卷 205-226页

作者： Priyam Mitra heng lian Ritwik Mitra Hua liang Min-ge Xie Department of Statistics and Biostatistics Rutgers University Department of Mathematics City University of Hong Kong Department of Operations Research and Financial Engineering Princeton University Department of Statistics George Washington University

Model selection strategies have been routinely employed to determine a model for data analysis in statistics, and further study and inference then often proceed as though the selected model were the true model that were known a priori. Model averaging approaches, on the other hand, try to combine estimators for a set of candidate models. Specifically, instead of deciding which model is the 'right' one, a model averaging approach suggests to fit a set of candidate models and average over the estimators using data adaptive *** this paper we establish a general frequentist model averaging framework that does not set any restrictions on the set of candidate models. It broaden, the scope of the existing methodologies under the frequentist model averaging development. Assuming the data is from an unknown model, we derive the model averaging estimator and study its limiting distributions and related predictions while taking possible modeling biases into *** propose a set of optimal weights to combine the individual estimators so that the expected mean squared error of the average estimator is minimized. Simulation studies are conducted to compare the performance of the estimator with that of the existing methods. The results show the benefits of the proposed approach over traditional model selection approaches as well as existing model averaging methods.

关键词： asymptotic distribution bias variance trade-off local mis-specification model averaging estimators optimal weight selection