空間變異係數模型

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姓名

黃冠綾(Kuan-Ling Huang) 查詢紙本館藏

畢業系所

統計研究所

論文名稱

空間變異係數模型
(Study on the spatially varying coefficient models)

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至系統瀏覽論文 (2025-7-1以後開放)

摘要(中)

空間統計學中，如何透過有限的抽樣點資料對未抽樣的位置進行空間預測是感興趣且重要的議題。不同於一般的固定係數空間迴歸模型，本文透過平滑樣條(smoothing splines)函數提出變異係數空間迴歸模型。模型中，我們考慮迴歸係數可隨地理位置變化並設計二階段的演算法估計迴歸係數曲面及模型參數，進而得到研究區域的空間預測曲面。本文亦透過統計假設檢定，讓資料自動決定該使用變異係數或固定係數的空間迴歸模型。完整的數值模擬實驗呈現並比較兩種空間預測方法的表現，同時也藉由分析臺灣PM2.5濃度的數據說明所提方法的實用性。

摘要(英)

In spatial statistics, how to make spatial prediction for unsampled locations based on observed noisy data is an interesting and important issue. Different from general spatial regression models with fixed regression coefficients, this thesis proposes a spatially varying coefficient regression model via a smoothing spline technique, where the regression coefficients are allowed to vary with geographic locations. A two-stage algorithm is designed to estimate regression coefficients as well as model parameters. Then, a predicted surface over the study region can be obtained. In practice, how to determine an appropriate method between the varying coefficient model and the fixed coefficient model is another important issue which can be solved by a statistical hypothesis test. Numerical results show the effectiveness of the proposed methodology and a real data example regarding the fine particulate matter (PM2.5) concentration in Taiwan is analyzed for illustration.

關鍵字(中)

★ 平滑樣條
★ 空間預測
★ 空間迴歸模型
★ 二階段參數估計

關鍵字(英)

★ Smoothing splines
★ Spatial prediction
★ Spatial regression model
★ Two-stage parameter estimation

論文目次

Contents
1 Introduction 1
2 Spatial regression model and spatial prediction 4
2.1 Spatial regression model........................... 4
2.2 Parameter estimation and spatial prediction........ 5
3 Proposed methodology 7
3.1 Model and methodology.............................. 7
3.2 Algorithm.......................................... 10
4 Hypothesis test 12
5 Simulation study 15
5.1 Simulation scenario 1.............................. 15
5.2 Simulation results for scenario 1.................. 21
5.3 Simulation scenario 2.............................. 25
5.4 Simulation results for scenario 2.................. 28
5.5 Comparisons and results............................ 30
6 A case study 33
7 Conclusion and discussion 40
Reference 42

參考文獻

Reference
Bradley, J., Cressie, N.,and Shi, T.(2013).Local spatial-predictor selection. Centre for Statistical and Survey Methodology, University of Wollongong, Working Paper, 13, 9-
13.
Chen, C.S. and Chen, C.S. (2018). A composite spatial predictor via local criteria under a misspecified model. Stochastic Environmental Research and Risk Assessment, 32,
341-355.
Chen, L.J., Ho, Y.H., Lee, H.C., Wu, H.C., Liu, H.M., Hsieh, H.H., Huang, Y.T.,and Candice Lung, S.C. (2017). An Open Framework for Participatory PM2.5 Monitoring in Smart Cities. IEEE Access Journal, 5, 14441-14454.
Craven, P. and Wahba, G.(1979). Smoothing noisy data with spline functions:Estimating the correct degree of smoothing by the method of generalized cross-validation. Numerische Mathematik, 31, 377-403.
Cressie, N.(1993). Statistics for Spatial Data (revised edition), Wiley: NewYork.
Cressie, N. and Lahiri, S.N.(1996). Asymptotics for REML estimation of spatial covariance parameters. J Stat Plan Inference, 50, 327-341.
Johnson, R.A. and Wichern, D.W.(2007). Applied Multivariate Statistical Analysis (6th edition), PrenticeHall: Hoboken.
Mat´ern,B.(2013). Spatial variation, Springer: Berlin.
McGilchrist, C.A.(1989). Bias of ML and REML estimators in regression models with ARMA errors. Journal of Statistical Computation and Simulation, 32, 127-136.
Mu, J.,Wang, G.,and Wang, L.(2018). Estimation and inference in spatially varying coefficient models. Environmetrics, 29:e2485.
Patterson, H.D. and Thompson, R.(1971).Recovery of Inter-Block Information When Block Size Are Unequal. Biometrika, 58, 545-554.
Schabenberger, O. and Gotway, C.A.(2005). Statistical Methods for Spatial Data Analysis, Chapman &Hall/CRC Press.
Shen, S.L., Mei, C.L.,and Zhang, Y.J.(2011).Spatially varying coefficient models: Testing for spatial heteroscedasticity and reweighting estimation of the coefficients. Environment and Planning A, 43, 1723-1745.
Wecker, W. and Ansley, C.(1983). The signal extraction approach to nonlinear regression and spline smoothing. Journal of the American Statistical Association, 78, 81-89.
Yang, H.D. and Chen,C.S.(2017). On estimation and prediction of geostatistical regression models via a corrected Stein’s unbiased risk estimator. Environmetrics, 28:e2424.

指導教授

陳春樹(Chun-Shu Chen)

審核日期

2022-6-24

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