In this paper, we propose a simple linear least squares framework to deal with estimation and selection for a groupwise additive multiple-index model, of which the partially linear single-index model is a special case, and in which each component function has a single-index structure. We show that, somewhat unexpectedly, all index vectors can be recovered through a single least squares coefficient vector. As a direct application, for partially linear single-index models we develop a new two-stage estimation procedure that is iterative-free and easily implemented. This estimation approach can also be applied to develop, for the semi-parametric model under study, a penalized least squares estimation and establish its asymptotic behavior in sparse and high-dimensional settings without any nonparametric treatment. A simulation study and a real world data analysis are presented.
Extreme precipitation caused by global climate change is expected to have a severe impact on urbanized areas. While decision‐makers struggle with climate uncertainty, an effective infrastructure adaptation strategy attaches great importance to preventing disasters resulting from rainfall. We propose a decision‐making model to incorporate the probability of rainfall disasters and recommend investing time when evaluating projects related to climate adaptation. We use a hydrological statistical model and economic and technical factors to estimate the expected economic losses in several rainfall disaster scenarios, and the value of the adaptation infrastructures is calculated using a real options pricing approach. Then the decision‐making model is applied to a case study involving a campus rainfall disaster prevention facility at the Central University of Finance and Economics in Beijing, China. We established three submerged scenarios with different rainfall intensities, then we evaluated the premium of holding an option to defer and pointed out the optimal investing time in each scenario. This model is expected to provide guidance for the development of adaptation infrastructure for relatively small areas such as communities and universities. And we proved that using real options‐based approach could provide more managerial flexibility for investors.
This paper tries to explore a more applicable tradable credit scheme for managing network mobility from the angle of marginal cost pricing. The classic mathematical model-Cobweb model is used to analyze the stability of credit price. It is found that credit price is not always convergent in the trading market. It will show convergence, divergence, two-period simple behaviors, and even more complex dynamic behaviors, such as cycle movements and chaos. Considering the applicability and public goods character of tradable credits scheme, one public pricing mechanism- marginal cost pricing is explored. Analytical investigations and the numerical simulation of a particular case with linear demand and supply indicate that marginal cost pricing is an effective, sustainable, and socially feasible manner in managing the demand for car travel.
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