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研究生： 曾奕齊
Tseng, Yi-Chi
論文名稱： 高維度空間統計之模型選擇
Variable selection for high-dimensional spatial linear models
指導教授： 銀慶剛
Ing, Ching-Kang
口試委員: 黃文瀚
Hwang, Wen-Han
黃信誠
Huang, Hsin-Cheng
俞淑惠
Yu, Shu-Hui
學位類別： 碩士
Master
系所名稱： 理學院 - 統計學研究所
Institute of Statistics
論文出版年： 2019
畢業學年度： 108
語文別： 英文
論文頁數： 24
中文關鍵詞： 自我相關條件模型 、同步相關條件模型 、空間統計 、模型選擇 、高維度訊息準則 、正交貪婪演算法 、柴比雪夫貪婪演算法
外文關鍵詞： Conditional autoregressive model, simultaneous autoregressive model, spatial statistics
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    • 空間線性模型常用於分析空間格數據，特別是高維數據。我們回顧了朱、黃
    和Reyes 在2010 年提出的同時選擇模型與參數估計的統計方法，並嘗試將其用
    於高維數據。我們提出另一種不同的模型選擇方法，首先在迴歸部分使用正交
    貪婪演算法（OGA），而柴比雪夫貪婪演算法(CGA) 用於空間自迴歸部分選擇
    變數和鄰里結構。模擬結果及實例的房價數據分析比較了我們方法和其他方法
    的表現。讀者可以根據需要選擇最合適的空間線性模型以滿足他們的需求。

    Spatial linear models are popular for the analysis of spatial lattice data, in particular
    highdimensional
    data. We review the statistical techniques for simultaneous
    model selection and parameter estimation for spatial lattice data proposed
    by Zhu, Huang and Reyes in 2010, and attempt to use them for highdimensional
    data. We propose different methods for model selection, including the orthogonal
    greedy algorithm (OGA) for the regression part, and the Chebyshev greedy algorithm
    for the autoregressive
    part to select covariates and a neighborhood structure.
    Simulation results and applications to real house price data demonstrate the performance
    of the proposed approach compared with others. Users can choose the
    most suitable spatial linear model according to their needs.

    Contents 1 Introduction 1 2 Model 3 3 Model Selection 6 4 Simulation 10 4.1 Case 1 . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 12 4.2 Case 2 . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 15 5 Real Data Analysis 17 6 References 23

    ZHU, J., HUANG, H.C., and REYES, P. (2010). On selection of spatial linear models for lattice data. J. Roy. Statist. Soc. Ser. B, 72,389–402.
    CHEN, Y.L, DAI, C.S, and ING, C.K. (2019). HighDimensional
    Model Selection via Chebyshev Greedy Algorithms. Working paper. ING, C.K and LAI, T. L. (2011).
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    TIBSHIRANI, R. (1996). Regression shrinkage and selection via the lasso. J. R. Statist. Soc. B, 58, 267–288. 23
    ZOU, H. (2006). The adaptive LASSO and its oracle properties. J. Am. Statist. Ass., 101,1418–1429.
    EFRON,B., HASTIE,T., JOHNSTONE,I., and TIBSHIRANI,R. (2004). Least angle regression. Ann. Statist., 32,407–499.
    CRESSIE, N. (1993). Statistics for Spatial Data , revised ed. Wiley, New York.
    SCHABENBERGER, O. and GOTWAY, C.A. (2005). Statistical Methods for Spatial Data Analysis. Chapman and Hall, Boca Raton.
    R.A. DUBIN, (1988). Estimation of regression coefficients in the presence of spatially autocorrelated error terms, Rev. Econom. Statist., 70,466–474.
    WHITTLE, P. (1954). On Stationary processes in the plane. Biometrika, 41,431– 449

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