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
Actions and policies to enhance biodiversity in the urban landscape must match the spatial scale at which biodiversity responds to the management and target variables. To this end, we compare the importance and effect of different kinds of greenery cover and road-lane density on bird and butterfly species richness between two landscape scales: 50-m versus 126-m radii around point counts (equivalent to areas of 0.8 h and 5 ha, respectively). We also compared the results against those of an earlier study using 500-m walking transects with widths of 100 m (i.e., 5 ha). Road lane density was more important at the 126-m than 50-m radius for both birds and butterflies. For birds, natural vegetation or forest cover and cultivated shrub cover were also more important at 126-m radius whereas the cultivated tree canopy cover was more important at 50-m radius. Cultivated tree cover and natural vegetation or forest cover were positively associated with species richness while road lane density and cultivated shrub cover were negatively associated with species richness. The results from point counts generally corroborate the results from the transects-based study, except that the short-duration point counts performed poorly in sampling butterflies. Our results indicate that in designing urban greenery policy, the plot sizes of individual developments is an appropriate spatial scale for the stipulation of tree cover targets, while urban planners have more flexibility to allocate natural greenery at broader spatial scales.