A Sequential Shrinkage Estimating Method for Tobit Regression Model

In the applications of Tobit regression models we always encounter the data sets which contain too many variables that only a few of them contribute to the model. Therefore, it will waste much more samples to estimate the “non-effective” variables in the inference. In this paper, we use a sequential procedure for constructing the fixed size confidence set for the “effective” parameters to the model by using an adaptive shrinkage estimate such that the “effective” coefficients can be efficiently identified with the minimum sample size based on Tobit regression model. Fixed design is considered for numerical simulation.

Sequential Shrinkage Estimate for COX Regression Models with Uncertain Number of Effective Variables

In the applications of COX regression models, we always encounter data sets that contain too many variables that only a few of them contribute to the model. Therefore, it will waste much more samples to estimate the “noneffective” variables in the inference. In this paper, we use a sequential procedure for constructing the fixed size confidence set for the “effective” parameters to the model based on an adaptive shrinkage estimate such that the “effective” coefficients can be efficiently identified with the minimum sample size. Fixed design is considered for numerical simulation. The strong consistency, asymptotic distributions and convergence rates of estimates under the fixed design are obtained. In addition, the sequential procedure is shown to be asymptotically optimal in the sense of Chow and Robbins (1965).

线性回归模型中相依数据的多结构变点的估计

多变点线性模型经常应用于统计学和计量经济学中.本文通过分割数据并建立相依观测数据的高维线性回归模型,将变点检测问题转化为变量选择问题.在变量选择中,应用组正交贪婪算法(group orthogonal greedy algorithm,GOGA)来解决变点数量随观测数量的增加而增加的情形,并结合高维信息准则(high-dimensional information criteria,HDIC)以防止过度拟合.第一阶段采用GOGA+HDIC+Trim对分段数据进行变量选择来降低计算成本,第二阶段应用拟似然比检验来得到更精准的变点位置.在相对温和的条件下,本文证明了变点数量和位置的相合性.模拟结果和实际数据应用证明了该算法的精确性.