Cheng Xu

The scaling law is a functional relationship between two parameters. In the field of urban studies, the distribution of various phenomena follows the scaling law, e.g., travel time, travel distance, and visitation frequency. To capture the scaling law of spatial visitation frequency on a motorized vehicle, this study carried out a numerical study based on the license plate recognition (LPR) data of three cities, Hangzhou, Guiyang, and Xiaoshan in China. Firstly, according to the LPR data, vehicles are classified into different types, including foreign vehicles, on-demand ride-sourcing cars, and taxis. Then, the spatial visitation frequency of different vehicle types, different cities, and different time periods was calculated. The results show that the scaling law of the spatial visitation frequency always conforms to the exponential function, no matter the city types, time periods, or type of vehicles.

This paper studies the averaging GMM estimator that combines a conservative GMM estimator based on valid moment conditions and an aggressive GMM estimator based on both valid and possibly misspecified moment conditions, where the weight is the sample analog of an infeasible optimal weight. We establish asymptotic theory on uniform approximation of the upper and lower bounds of the finite‐sample truncated risk difference between any two estimators, which is used to compare the averaging GMM estimator and the conservative GMM estimator. Under some sufficient conditions, we show that the asymptotic lower bound of the truncated risk difference between the averaging estimator and the conservative estimator is strictly less than zero, while the asymptotic upper bound is zero uniformly over any degree of misspecification. The results apply to quadratic loss functions. This uniform asymptotic dominance is established in non‐Gaussian semiparametric nonlinear models.