Abstract
Statistical methods are useful tools to deal with data on socioeconomic-technological systems. In this chapter, we will address fundamental expressions used in statistics and methods of data analysis: time series analysis, network analysis and spatial analysis.
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GADM database: www.gadm.org.
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Appendices
Appendix A: Proof of \(0\ln 0\)
Let us consider
Putting \(x = e^{-z}\) one has
By using the Taylor expansion of \(e^{z} = \sum _{k=0}^{\infty }\frac{1}{k!}z^k\), one obtains
Therefore, we gets
Appendix B: Derivation of the Mean Square Error of RMA Regression
The mean square error \(MSE\) of the RMA regression is defined as
Inserting Eq. (3.70) into Eq. (3.258), we get
This is also written as
Inserting Eq. (3.74) into Eq. (3.260), consequently we obtain
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Sato, AH. (2014). Mathematical Expressions. In: Applied Data-Centric Social Sciences. Springer, Tokyo. https://doi.org/10.1007/978-4-431-54974-1_3
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