克利金模型中基於Kullback-Leibler損失的共變異函數選擇

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賴堉溱(Yu-Chen Lai) 查詢紙本館藏

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統計研究所

論文名稱

克利金模型中基於Kullback-Leibler損失的共變異函數選擇
(Covariance Function Selection in Kriging Models Using Kullback-Leibler Loss)

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至系統瀏覽論文 (2026-8-1以後開放)

摘要(中)

在空間統計領域中，克利金（kriging）模型被廣泛應用於預測空間中感興趣的隨機變數，包括沒有觀測數據的位置。然而，這種預測方法依賴於空間相關函數的使用，而這些函數直接影響克利金預測結果的表現。本篇論文欲透過結合各種協方差函數於克利金空間模型中，探討空間相關函數對預測結果的影響。我們使用Kullback-Leibler 損失準則來評估克利金模型的表現，並透過數據擾動技術來估計和量化克里金模型的預測複雜性。基於此，我們提出了一個用於選擇適當協方差函數的準則。所提方法的有效性將透過多種模擬實驗驗證，並且我們將該方法應用於分析台灣的空氣品質數據，以說明其實用性。

摘要(英)

In the field of spatial statistics, kriging models are frequently utilized for predicting variables of interest across a study region, including in areas without observational data, based on noise data observed at specific locations. The use of spatial correlation functions plays a crucial role in this context, as they directly impact
the accuracy of kriging predictions. This thesis attempts to address this challenge by exploring the use of different covariance functions within spatial models. The performance of spatial kriging models employing various covariance functions is evaluated using the Kullback-Leibler loss criterion. Moreover, we measure the complexity of any spatial prediction method through the concept of generalized degrees of freedom, estimated using data perturbation techniques. Consequently, an estimated Kullback-Leibler loss criterion is proposed for selecting an appropriate covariance function. Focusing on spatial prediction, the effectiveness of the proposed method is validated through simulation experiments, and its practical utility is demonstrated using air quality data from Taiwan.

關鍵字(中)

★ 空氣品質
★ 資料擾動
★ Kullback-Leibler 損失
★ 均方預測誤差
★ 參數估計

關鍵字(英)

★ Air quality
★ Data perturbation
★ Kullback-Leibler loss
★ Mean squared prediction error
★ Parameter estimation

論文目次

摘要I
Abstract II
誌謝III
Contents IV
List of Figures V
List of Tables VII
1 Introduction 1
2 Geostatistical Models 4
2.1 Model Settings . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 4
2.2 Covariance Functions . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 5
2.3 Spatial Prediction and Parameter Estimation . . . . . . . . . . . . . . . . . . . 8
3 Selection of Covariance Functions 13
3.1 Kullbeck–Leibler Loss . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 13
3.2 Data Perturbation . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 15
3.3 Covariance Selection Criterion . . . . . . . . . . . . . . . . . . . . . . . . . . 17
4 Simulations Study 19
4.1 Setups . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 19
4.2 Results . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 22
5 Application: Air Quality Data 30
6 Conclusion 38
References 40

參考文獻

Altman, N. (2000). Krige, smooth, both or neither? Australian & New Zealand Journal of Statistics, 42, 441-461.

Box, G. E. P. and Cox, D. R. (1964). An analysis of transformations. Journal of the Royal Statistical Society. Series B (Methodological), 26, 211-252.

Chen, C. S., Yang, H. D., and Li, Y. (2014). A stabilized and versatile spatial prediction method for geostatistical models. Environmetrics, 25, 127-141.

Cressie, N. (1993). Statistics for Spatial Data (revised ed.), Wiley, New York.

Cressie, N. and Lahiri, S. N. (1993). On information and sufficiency. Journal of Multivariate Analysis, 45, 217-233.

Huang, H. C. and Chen, C. S. (2007). Optimal geostatistical model selection. Journal of the American Statistical Association, 102, 1009-1024.

Kullback, S. and Leibler, R. A. (1951). The asymptotic distribution of REML estimators. The Annals of Mathematical Statistics, 22(1), 79-86.

Lin, C. A., Chen, Y. C., Liu, C. Y., Chen, W. T., Seinfeld, J. H. and Chou, C. K. (2019). Satellite-derived correlation of SO2, NO2, and aerosol optical depth with meteorological
conditions over east Asia from 2005 to 2015. Remote Sens, 11, 17-38.

Matérn, B. (1986). Spatial Variation (second edition), Lecture Notes in Statistics, Springer: New York.

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.

Patterson, H. D. and Thompson, R. (1971). Recovery of inter-block information when block sizes are unequal. Biometrika, 58, 545-554.

Shen, X., Huang, H. C. and Ye, J. (2004). Adaptive model selection and assessment for exponential family models. Technometrics, 46, 306-317.

Shen, X. and Ye, J. (2002). Adaptive model selection. Journal of the American Statistical Association, 97, 210-221.

Wang, Y. (1998). Smoothing spline models with correlated random errors. Journal of the American Statistical Association, 93, 341-348.

Ye, J. (1998). On measuring and correcting the effects of data mining and model selection. Journal of the American Statistical Association, 93, 120-131.

指導教授

陳春樹(Chun-Shu Chen)

審核日期

2024-7-3

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