The Student-t regression model is a useful extension of the normal model,which can be used for statistical modeling of data sets involving errors with heavy tails and/or outliers and provides robust estimation of mean...The Student-t regression model is a useful extension of the normal model,which can be used for statistical modeling of data sets involving errors with heavy tails and/or outliers and provides robust estimation of means and regression coefficients.In this paper,the varying dispersion Student-t regression model is discussed,in which both the mean and the dispersion depend upon explanatory variables.The problem of interest is simultaneously select significant variables both in mean and dispersion model.A unified procedure which can simultaneously select significant variable is given.With appropriate selection of the tuning parameters,the consistency and the oracle property of the regularized estimators are established.Both the simulation study and two real data examples are used to illustrate the proposed methodologies.展开更多
This study examined how the signals of interest （SOI） effect on the backscattering measurement numerically based on 3-D finite-difference time-domain （FDTD） method. High resolution microstructure mappings of bovin...This study examined how the signals of interest （SOI） effect on the backscattering measurement numerically based on 3-D finite-difference time-domain （FDTD） method. High resolution microstructure mappings of bovine cancellous bones provided by micro-CT were used as the input geometry for simulations. Backscatter coefficient （BSC）, integrated backscatter coefficient （IBC） and apparent integrated backscatter （AIB） were calculated with changing the start （L1） and duration （L2） of the SOl. The results demonstrated that BSC and IBC decrease as L1 increases, and AIB decreases more rapidly as L1 increases. The backscattering parameters increase with fluctuations as a function of L2 when L2 is less than 6 mm. However, BSC and IBC change little as L2 continues to increase, while AIB slowly decreases as L2 continues to increase. The results showed how the selections of the SOI effect on the backscattering measurement. An explicit standard for SOl selection was proposed in this study and short L1 （about 1.5 mm） and appropriate L2 （6 mm-12 mm） were recommended for the calculations of backscattering parameters.展开更多
We study a second-order parabolic equation with divergence form elliptic operator,having a piecewise constant diffusion coefficient with two points of discontinuity.Such partial differential equations appear in the mo...We study a second-order parabolic equation with divergence form elliptic operator,having a piecewise constant diffusion coefficient with two points of discontinuity.Such partial differential equations appear in the modelization of diffusion phenomena in medium consisting of three kinds of materials.Using probabilistic methods,we present an explicit expression of the fundamental solution under certain conditions.We also derive small-time asymptotic expansion of the PDE’s solutions in the general case.The obtained results are directly usable in applications.展开更多
基金supported in part by the National Natural Science Foundation of China under Grant Nos.11171112,11101114,11201190the National Statistical Science Research Major Program of China under Grant No.2011LZ051+4 种基金the 111 Project of China under Grant No.B14019the Doctoral Fund of Ministry of Education of China under Grant No.20130076110004the Natural Science Project of Jiangsu Province Education Department under Grant No.13KJB110024the Natural Science Fund of Nantong University under Grant No.13ZY001the Research Project of Social Science and Humanity Fund of the Ministry of Education under Grant No.14YJC910007
文摘The Student-t regression model is a useful extension of the normal model,which can be used for statistical modeling of data sets involving errors with heavy tails and/or outliers and provides robust estimation of means and regression coefficients.In this paper,the varying dispersion Student-t regression model is discussed,in which both the mean and the dispersion depend upon explanatory variables.The problem of interest is simultaneously select significant variables both in mean and dispersion model.A unified procedure which can simultaneously select significant variable is given.With appropriate selection of the tuning parameters,the consistency and the oracle property of the regularized estimators are established.Both the simulation study and two real data examples are used to illustrate the proposed methodologies.
基金supported by the National Natural Science Foundation of China(Grant No. 11174060)the Ph.D. Programs Foundation of the Ministry of Education of China(Grant Nos. 20090071110066,20110071130004)+1 种基金the Key Science and Technology Program of Shanghai(Grant No. 09441900400)the Program for New Century Excellent Talents in University(Grant No. NCET-10-0349)
文摘This study examined how the signals of interest （SOI） effect on the backscattering measurement numerically based on 3-D finite-difference time-domain （FDTD） method. High resolution microstructure mappings of bovine cancellous bones provided by micro-CT were used as the input geometry for simulations. Backscatter coefficient （BSC）, integrated backscatter coefficient （IBC） and apparent integrated backscatter （AIB） were calculated with changing the start （L1） and duration （L2） of the SOl. The results demonstrated that BSC and IBC decrease as L1 increases, and AIB decreases more rapidly as L1 increases. The backscattering parameters increase with fluctuations as a function of L2 when L2 is less than 6 mm. However, BSC and IBC change little as L2 continues to increase, while AIB slowly decreases as L2 continues to increase. The results showed how the selections of the SOI effect on the backscattering measurement. An explicit standard for SOl selection was proposed in this study and short L1 （about 1.5 mm） and appropriate L2 （6 mm-12 mm） were recommended for the calculations of backscattering parameters.
基金supported by the National Science Foundation of USA (Grant No. DMS1206276)National Natural Science Foundation of China (Grant No. 1128101)the Research Unit of Tunisia (Grant No. UR11ES53)
文摘We study a second-order parabolic equation with divergence form elliptic operator,having a piecewise constant diffusion coefficient with two points of discontinuity.Such partial differential equations appear in the modelization of diffusion phenomena in medium consisting of three kinds of materials.Using probabilistic methods,we present an explicit expression of the fundamental solution under certain conditions.We also derive small-time asymptotic expansion of the PDE’s solutions in the general case.The obtained results are directly usable in applications.
