随着计算机的发展,函数型变量的数据收集变得越来越容易,传统的不等概抽样方法仅考虑了标量型的辅助变量,同时在不等概抽样方法中确定总体单元入样概率并不容易,为此提出了一种带有函数型变量的不等概抽样方法,这种不等概率抽样方法从...随着计算机的发展,函数型变量的数据收集变得越来越容易,传统的不等概抽样方法仅考虑了标量型的辅助变量,同时在不等概抽样方法中确定总体单元入样概率并不容易,为此提出了一种带有函数型变量的不等概抽样方法,这种不等概率抽样方法从样本数据中提取信息构造总体单元入样概率,克服了确定每个总体单元入样概率的困难。模拟结果表明带有函数型变量的不等概抽样估计结果优于简单随机抽样估计结果。最后将其应用到共享单车数据中得到带有函数型变量的不等概抽样的良好表现。With the development of computers, data collection for functional variables has become increasingly easy. Traditional inequality sampling methods only consider scalar auxiliary variables, and it is not easy to determine the sampling probability of population units in inequality sampling methods. Therefore, unequal Probability sampling method with functional variables is proposed. This unequal probability sampling method extracts information from sample data to construct the sampling probability of population units, overcoming the difficulty of determining the sampling probability of each population unit. The simulation results show that the estimation results of unequal probability sampling with functional variables are better than those of simple random sampling estimation. Finally, the method is applied to shared bicycle data and achieves good performance in unequal probability sampling with functional variables.展开更多
本文研究响应变量和预测因子均为向量的充分降维问题。投影重采样方法的核心思想是将多元响应投影到随机采样的方向上,以获取标量响应的样本,并反复应用单变量响应的降维方法来解决问题。该方法已被证明对多元线性降维有效。本文将投影...本文研究响应变量和预测因子均为向量的充分降维问题。投影重采样方法的核心思想是将多元响应投影到随机采样的方向上,以获取标量响应的样本,并反复应用单变量响应的降维方法来解决问题。该方法已被证明对多元线性降维有效。本文将投影重采样方法推广到非线性情境,并通过核映射提出了四种新的估计方法。研究结果表明,新方法具有优良的性质,并能在温和条件下完整恢复降维空间。最后,通过数值模拟和真实数据集分析验证了所提方法的有效性和可行性。This paper addresses the problem of sufficient dimension reduction where both the response and predictor are vectors. The core idea of projective resampling method is to project the multivariate responses along randomly sampled directions to obtain samples of scalar-valued responses. A univariate-response dimension reduction method is then applied repeatedly for solving the problem. This has proven effective for multivariate linear dimension reduction. In this paper, we extend the projective resampling method to nonlinear scenarios and use the mapping induced by kernels to develop four novel estimation methods. The research results suggest that the new methods exhibit excellent properties and ensure full recovery of the dimension reduction space under mild conditions. Finally, we validate the effectiveness and feasibility of the proposed methods through numerical simulations and real data analysis.展开更多
文摘随着计算机的发展,函数型变量的数据收集变得越来越容易,传统的不等概抽样方法仅考虑了标量型的辅助变量,同时在不等概抽样方法中确定总体单元入样概率并不容易,为此提出了一种带有函数型变量的不等概抽样方法,这种不等概率抽样方法从样本数据中提取信息构造总体单元入样概率,克服了确定每个总体单元入样概率的困难。模拟结果表明带有函数型变量的不等概抽样估计结果优于简单随机抽样估计结果。最后将其应用到共享单车数据中得到带有函数型变量的不等概抽样的良好表现。With the development of computers, data collection for functional variables has become increasingly easy. Traditional inequality sampling methods only consider scalar auxiliary variables, and it is not easy to determine the sampling probability of population units in inequality sampling methods. Therefore, unequal Probability sampling method with functional variables is proposed. This unequal probability sampling method extracts information from sample data to construct the sampling probability of population units, overcoming the difficulty of determining the sampling probability of each population unit. The simulation results show that the estimation results of unequal probability sampling with functional variables are better than those of simple random sampling estimation. Finally, the method is applied to shared bicycle data and achieves good performance in unequal probability sampling with functional variables.
文摘本文研究响应变量和预测因子均为向量的充分降维问题。投影重采样方法的核心思想是将多元响应投影到随机采样的方向上,以获取标量响应的样本,并反复应用单变量响应的降维方法来解决问题。该方法已被证明对多元线性降维有效。本文将投影重采样方法推广到非线性情境,并通过核映射提出了四种新的估计方法。研究结果表明,新方法具有优良的性质,并能在温和条件下完整恢复降维空间。最后,通过数值模拟和真实数据集分析验证了所提方法的有效性和可行性。This paper addresses the problem of sufficient dimension reduction where both the response and predictor are vectors. The core idea of projective resampling method is to project the multivariate responses along randomly sampled directions to obtain samples of scalar-valued responses. A univariate-response dimension reduction method is then applied repeatedly for solving the problem. This has proven effective for multivariate linear dimension reduction. In this paper, we extend the projective resampling method to nonlinear scenarios and use the mapping induced by kernels to develop four novel estimation methods. The research results suggest that the new methods exhibit excellent properties and ensure full recovery of the dimension reduction space under mild conditions. Finally, we validate the effectiveness and feasibility of the proposed methods through numerical simulations and real data analysis.
