An extended single‐index model is considered when responses are missing at random. A three‐step estimation procedure is developed to define an estimator for the single‐index parameter vector by a joint estimating equation. The proposed estimator is shown to be asymptotically normal. An algorithm for computing this estimator is proposed. This algorithm only involves one‐dimensional nonparametric smoothers, thereby avoiding the data sparsity problem caused by high model dimensionality. Some simulation studies are conducted to investigate the finite sample performances of the proposed estimators. 相似文献
The high-dimensional data arises in diverse fields of sciences, engineering and humanities. Variable selection plays an important role in dealing with high dimensional statistical modelling. In this article, we study the variable selection of quadratic approximation via the smoothly clipped absolute deviation (SCAD) penalty with a diverging number of parameters. We provide a unified method to select variables and estimate parameters for various of high dimensional models. Under appropriate conditions and with a proper regularization parameter, we show that the estimator has consistency and sparsity, and the estimators of nonzero coefficients enjoy the asymptotic normality as they would have if the zero coefficients were known in advance. In addition, under some mild conditions, we can obtain the global solution of the penalized objective function with the SCAD penalty. Numerical studies and a real data analysis are carried out to confirm the performance of the proposed method. 相似文献
Natural catastrophes such as earthquakes can, in addition to causing loss of life, disrupt the urbanization process through the need for forced population redistribution and the modification of resource and environmental carrying capacity. The population carrying capacity (PCC) of an altered environment following an earthquake is a crucial determinant in the relocation of displaced persons. We use data adaptive methods to model the correlation between the physical environment and human population density in estimating PCC in areas affected by the 2008 Wenchuan earthquake. Comparing actual population distributions with ideal population distributions allows for the identification of villages where population exceeds PCC, or conversely, areas where the environment can support a higher population. Such a comparison can provide the basis for a relocation plan, a critical element of post-catastrophe policy-making. 相似文献
The load-sharing model has been studied since the early 1940s to account for the stochastic dependence of components in a parallel system. It assumes that, as components fail one by one, the total workload applied to the system is shared by the remaining components and thus affects their performance. Such dependent systems have been studied in many engineering applications which include but are not limited to fiber composites, manufacturing, power plants, workload analysis of computing, software and hardware reliability, etc. Many statistical models have been proposed to analyze the impact of each redistribution of the workload; i.e., the changes on the hazard rate of each remaining component. However, they do not consider how long a surviving component has worked for prior to the redistribution. We name such load-sharing models as memoryless. To remedy this potential limitation, we propose a general framework for load-sharing models that account for the work history. Through simulation studies, we show that an inappropriate use of the memoryless assumption could lead to inaccurate inference on the impact of redistribution. Further, a real-data example of plasma display devices is analyzed to illustrate our methods.