臺灣博碩士論文加值系統

Variable selection is an active research topic and has attracted much attention in many scientific fields. However, if a variable selection process is unstable, inferences based on the selected model may be unreliable. To avoid the influence of selection instability, model averaging becomes a popular technique but has not received much attention especially for spatial regression models. In this thesis, we focus on discussing spatial regression model averaging based on conditional information criteria. We consider relatively few models for averaging, where a novel idea based on the values of information criteria is proposed to determine model weights. It results in the spatial predictor that is comparable to the conventional model averaging approaches and is computationally more efficient. Statistical inferences of the proposed methodology are justified both theoretically and numerically. Finally, an application of a mercury data set for lakes in Maine is analyzed for illustration.

Contents
1 Introduction 1
2 Spatial Regression and Its Prediction 4
2.1 Spatial Regression Models 4
2.2 Parameter Estimation 7
2.3 Spatial Prediction 8
3 Model Selection and Model Averaging 10
3.1 Spatial Predictor After Model Selection 10
3.2 Spatial Predictor After Model Averaging 12
4 The Proposed Methodology 14
4.1 GIC or CGIC in Spatial Regression 14
4.2 Novel Weights for Model Averaging 16
5 Simulation 19
5.1 Simulation Scenarios 19
5.2 Simulation Results 21
6 Application to Mercury Dataset 30
7 Conclusion and Discussion 34

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