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研究生:曾聖澧
論文名稱:多層解析混合自迴歸樹狀空間模型
論文名稱(外文):Autoregressive Tree-Structured Mixture Spatial Models
指導教授:黃信誠黃信誠引用關係陳志榮陳志榮引用關係
學位類別:碩士
校院名稱:國立交通大學
系所名稱:統計所
學門:數學及統計學門
學類:統計學類
論文種類:學術論文
論文出版年:2002
畢業學年度:90
語文別:英文
論文頁數:31
中文關鍵詞:多層解析資料分析樹狀模型大量資料時空模型空間統計臭氧
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本論文提出多層解析混合自迴歸樹狀空間模型、及其預測空間資料的快速
演算法。此一新方法根源於自迴歸樹狀模型,但單一自迴歸樹狀模型的缺點是其預測值會有塊狀叢聚現象。本文提出的混合自迴歸樹狀空間模型,具有平穩的空間共變異結構,因此其預測值不會出現塊狀現象。根據該模型可導證出一快速演算法用於處理大量空間資料,當資料中有遺漏值時,並不會影響其計算速度。該模型的另一項優點是可以 EM 演算法迭代求得其參數的最大概似估計量。此外,在實際問題中,選擇適合的模型對於預測舉足輕重,但相關文獻卻付之闕如。本文將討論如何以加權最小平方判則進行模型篩選。
In this article, we propose an autoregressive tree-structured mixture model and develop a computationally efficient algorithm for spatial prediction. The algorithm allows us to handle a huge dataset, even when there are missing observations. The
proposed mixture model has a stationary covariance structure and is free from blocky artifacts in prediction, which may be produced by a single autoregressive tree-structured model. We shall also show how to obtain the maximum likelihood estimators of the model parameters using an EM algorithm, and develop a model-selection criterion, which has not been addressed in the past literature.
Contents
1 Introduction 1
2 Autoregressive Tree-structured Models for Spatial Data 3
3 Autoregressive Tree-structured Mixture Models 6
3.1 The Model . . . . . . . . . . . . . . . . . . . . . . . 6
3.2 A Fast Spatial Prediction Algorithm . . . . . . . . . . 9
3.3 Parameter Estimation . . . . . . . . . . . . . . . . . . 12
3.4 Model Selection . . . . . . . . . . . . . . . . . . . . 14
4 An illustrated Example 15
5 Discussion 21
Appendix A 23
Appendix B 27
References 30
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