In high-dimensional linear regression, the dimension of variables is always greater than the sample size. In this situation, the traditional variance estimation technique based on ordinary least squares constantly exhibits a high bias even under sparsity assumption. One of the major reasons is the high spurious correlation between unobserved realized noise and several predictors. To alleviate this problem, a refitted cross-validation (RCV) method has been proposed in the literature. However, for a complicated model, the RCV exhibits a lower probability that the selected model includes the true model in case of finite samples. This phenomenon may easily result in a large bias of variance estimation. Thus, a model selection method based on the ranks of the frequency of occurrences in six votes from a blocked 3×2 cross-validation is proposed in this study. The proposed method has a considerably larger probability of including the true model in practice than the RCV method. The variance estimation obtained using the model selected by the proposed method also shows a lower bias and a smaller variance. Furthermore, theoretical analysis proves the asymptotic normality property of the proposed variance estimation. 相似文献
This paper studies the outlier detection and robust variable selection problem in the linear regression model. The penalized weighted least absolute deviation (PWLAD) regression estimation method and the adaptive least absolute shrinkage and selection operator (LASSO) are combined to simultaneously achieve outlier detection, and robust variable selection. An iterative algorithm is proposed to solve the proposed optimization problem. Monte Carlo studies are evaluated the finite-sample performance of the proposed methods. The results indicate that the finite sample performance of the proposed methods performs better than that of the existing methods when there are leverage points or outliers in the response variable or explanatory variables. Finally, we apply the proposed methodology to analyze two real datasets. 相似文献
High population growth in the tropics is driving urbanisation, removing diverse natural ecosystems. This is causing native species to suffer while introduced synanthropes flourish. City planners are developing urban greenspace networks, in part trying to address this issue. Architects contribute to these greenspace networks by designing elevated and ground level green spaces on large-scale buildings. However, little evidence is available on whether building green spaces support native fauna. This is true for birds in tropical Singapore that support important ecosystem services and have existence value. Therefore, in this study, we conducted bird surveys and statistical analyses to determine, if and how vegetation on three building green space types (ground gardens, roof gardens and green walls) have a positive impact on native or introduced bird species. We found that elevated greenery (roof gardens and green walls) on large-scale buildings supported a higher richness of birds and abundance of urban native birds than control roofs and walls without vegetation. Ground gardens supported similar levels of native species as roof gardens but also a larger proportion of generalist synanthropes. However, we found no tropical forest habitat specialists across any space type. Therefore, we recommend roof gardens and ground gardens as a potential space for urban natives outside of a less competitive ground-level urban environment. Our study also found certain building design elements (height of elevated space, presence of specific plants) supported different species groups. Therefore, we suggest that these ecological requirements for different species groups are considered when designing a building’s green space.
