Major Cities In China
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Our statistical framework for measuring the directional dependence is based on the following two assumptions. First, we assume that the four cities are subject to different pressures such as transportation, coal burning, or industrial activities. The consequences of this are not reflected in the statistical dependence between the cities, but we can detect it by analyzing the raw air pollution data. Second, we assume that the measurements at the city level are not independent. They are subject to the pressure from neighboring cities. That is, the air pollution levels at one city (e.g., city A) depend on the air pollution levels at neighboring cities (e.g., city B). Hence, the analysis can be done at the city level and not the individual city.
The above assumption leads us to formulate the analysis model as follows. Let $Y_{i}$ be the PM2.5 level measured at city A and $X_{i}$ be the PM2.5 level measured at city B. We consider city pair (A, B) and examine their dependence with respect to the covariate $Z_{i}$, where $Z_{i}$ is a binary variable that represents the city pair (A, B). We consider the following generalized linear model (GLM) without the intercept:
We are motivated by two main questions in this work. The first question is how to assess statistical dependence among the four cities, which is important for the study of multi-region air pollution. The second question is whether to use the data measured at the city level or the air pollution data collected at ground level for these analyses.
In the next section, we first introduce the statistical framework that we use to analyze the data measured at the city level. We then explain how we can estimate the air pollution data measured at the ground level. We present the results and implications of the analyses in the next section. In the last section, we provide some more discussion of the results.
We considered the following two hypotheses:
A hypothesis of no structural causality: The target cities are not connected to each other by any structural causality.
A hypothesis of structural causality: There is a direct causal link between the target cities.
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