半參數空間模型於所得分配不均資料之應用

Semiparametric Spatial Model for Income Inequality Data

黄佩新(Pei-Hsin Huang)

指導教授 ： 張雅梅

淡江大學/商管學院/統計學系應用統計學碩士班/碩士(2020年)

https://doi.org/10.6846/TKU.2020.00441

摘要

本研究提出一個非平穩半參數空間模型(non-stationary semi-parametric spatial model)來描述所得分配不均於空間上的相依性。該模型為數個基底函數(basis function)及平穩過程(stationary process)的線性組合，由於此模型有大量參數需要估計，我們使用Tibshirani (1996)提出的最小絕對壓縮與篩選運算法(least absolute shrinkage and selection operator, lasso)進行參數估計，該方法可以同時估計參數及作變數選取。接著使用Efron et al. (2001)提出的最小角迴歸法(least angle regression, lars)求lasso估計值，並利用交叉驗證法(cross-validation, cv)選擇lasso模型裡最適合的調整參數(tuning parameter)。本研究將估計結果繪製成空間分佈圖，透過空間分佈圖來描述歐洲地區所得分配不均資料在空間上的分佈情形。根據研究結果顯示，波羅地海三小國：愛沙尼亞(Estonia)、拉脫維亞(Latvia)及立陶宛(Lithuania)的變異程度較大；所得分配不均於愛沙尼亞(Estonia)和瑞典(Sweden)附近有較高的相依性，在德國(Germany)、英國(UK)及西班牙(Spain)附近相依性較低。

關鍵字

所得分配不均 ； 非平穩空間模型 ； 最小絕對壓縮與篩選運算法 ； 最小角迴歸法 ； 空間分佈

並列摘要

In this paper, we propose a non-stationary semi-parametric spatial model to describe the spatial dependence for the income inequality data in Europe. The model is presented by a linear combination of some basis functions and some stationary porcesses. We use least absolute shrinkage and selection operator (lasso, Tibshirani. 2006) to estimate the parameters. Lasso is very efficient because it can select and estimate parameters simultaneously. The least angle regression (lars, Efron et al. 2001) is used to solve the lasso estimates. The tuning parameter of lasso is selected by cross-validation (cv). In this research, the spatial dependence of the income inequality data in Europe is demonstrated by plots. According to our results, Baltic states: Estonia, Latvia and Lithuania have higher variances in income inequality. The correlation of income inequality in Estonia and Sweden to other countries is higher. Moreover, the correlation of income inequality in Germany, UK and Spain to other countries is lower. The results present a non-stationary structure of the income inequality data.

並列關鍵字

Income inequality ； non-stationary spatial model ； lasso ； lars ； spatial distribution

參考文獻

[1] Abdullah, A., Doucouliagos, H., and Manning, E. (2013), ”Does Education Reduce Income Inequality? A Meta-Regression Analysis,” Journal of Economic Surveys, 29, 301–316.

[2] Baumont, C., Ertur, C., and Gallo, J. L. (2003),

”Spatial Convergence Clubs and the European Regional Growth Process, 1980-1995,” Advance in Spatial Science, 131–158.

[3] Chakravorty, S. (1996), ”A Measurement of Spatial Disparity: The Case of Income Inequality,” Urban Studies, 33, 1671–1686.

[4] Chang., Y.-M., Hsu., N.-J., and Huang., H.-C. (2010), ”Semiparametric estimation and selection for nonstationary spatial covariance functions,” Journal of Computational and Graphical Statistics, 19, 117-139.