An Urban Scaling Estimation Method in a Heterogeneity Variance Perspective.

Area of Science:

• Urban studies
• Statistical modeling
• Complexity science

Background:

• Urban scaling laws reveal universal patterns in city growth.
• Accurate statistical estimation of scaling exponents remains challenging.
• Understanding variance properties is crucial for reliable urban scaling analysis.

Purpose of the Study:

• To propose a novel statistical regression method for urban scaling estimation.
• To address challenges in precise scaling exponent estimation, including lower bound constraints and heterogeneous variance.
• To enhance the accuracy and robustness of urban scaling studies.

Main Methods:

• Developed the Constrained Heterogeneous Variance Regression (CHVR) method.
• Employed maximum likelihood estimation with lower bound constraints.
• Modeled heterogeneous variance using a power-of-the-mean variance model.

Main Results:

• The CHVR method demonstrated superior effectiveness and robustness compared to traditional methods in estimating urban scaling exponents for six attributes in China.
• The proposed heterogeneous variance function accurately describes empirical data heterogeneity.
• Statistical tests confirmed the validity and informativeness of the variance function.

Conclusions:

• The CHVR method offers a valuable tool for precise and robust urban scaling estimations.
• This approach has significant potential for urban studies globally.
• The methodology can be extended to scaling law estimation in other complex systems.