A new reproducing kernel-based nonlinear dimension reduction method for survival data

Based on the theories of sliced inverse regression (SIR) and reproducing kernel Hilbert space (RKHS), a new approach RDSIR (RKHS-based Double SIR) to nonlinear dimension reduction for survival data is proposed. An isometric isomorphism is constructed based on the RKHS property, then the nonlinear function in the RKHS can be represented by the inner product of two elements that reside in the isomorphic feature space. Due to the censorship of survival data, double slicing is used to estimate the weight function to adjust for the censoring bias. The nonlinear sufficient dimension reduction (SDR) subspace is estimated by a generalized eigen-decomposition problem. The asymptotic property of the estimator is established based on the perturbation theory. Finally, the performance of RDSIR is illustrated on simulated and real data. The numerical results show that RDSIR is comparable with the linear SDR method. Most importantly, RDSIR can also effectively extract nonlinearity from survival data.     

基于对偶犹豫模糊几何Heronian平均算子的多属性决策方法及其应用

针对需要同时考虑变量隶属度、非隶属度以及关联性的融合问题，本文将对偶犹豫模糊集与Heronian平均算子相结合，定义了对偶犹豫模糊几何Heronian平均算子和对偶犹豫模糊几何加权Heronian平均算子，讨论了新算子的一些优良特性，包括幂等性、置换不变性、有界性、单调性等性质，并针对属性值为对偶犹豫模糊语言信息关联系的多属性决策问题，建立了基于对偶犹豫模糊几何加权Heronian平均算子的多属性决策模型，基于所定义的算子和建立的数学模型，提出了一种新的基于对偶犹豫模糊Heronian平均算子的多属性决策方法。最后，通过多属性决策算例验证了方法的有效性和可行性。     

The Dynamics of Inequality

The past forty years have seen a rapid rise in top income inequality in the United States. While there is a large number of existing theories of the Pareto tail of the long‐run income distributions, almost none of these address the fast rise in top inequality observed in the data. We show that standard theories, which build on a random growth mechanism, generate transition dynamics that are too slow relative to those observed in the data. We then suggest two parsimonious deviations from the canonical model that can explain such changes: “scale dependence” that may arise from changes in skill prices, and “type dependence,” that is, the presence of some “high‐growth types.” These deviations are consistent with theories in which the increase in top income inequality is driven by the rise of “superstar” entrepreneurs or managers.