臺灣博碩士論文加值系統

本篇論文提出兩個WIC的修正準則，WICu和WICs，做為在自我相關模式中階次選取的準則。WICu是由AICu和BIC所組成，在大樣本時相當於BIC，而在小樣本時相當於AICu，類似地，WICs是由AICu和SICc所組成，在大樣本時相當於SICc，在小樣本時會接近AICu。WICu和WICs在一般的條件下是具有一致性的準則。論文中並用模擬的方法將WICu及WICs和其他模式選取準則作比較，發現WICu和WICs在小樣本時的表現和AICu一樣，而且優於其他準則。大樣本時，WICu的表現和BIC一樣、WICs的表現和SICc一樣，並優於其他準則。

We proposed two modified weighted information criteria （WIC）, WICu and WICs, combining AICu with BIC and SICc, respectively, for order selection in autoregressive model. WICu is essentially equivalent to AICu for small sample sizes and to BIC for large sample sizes. Similarly, WICs is equivalent to SICc for large sample sizes and close to AICu for small sample sizes. Both of them are weakly consistent under general conditions. We also compare WICu and WICs with several popular criteria by simulation study. It shows WICu and WICs are better or at least comparable to WIC. In particular, for small samples, WICu and WICs perform as well as AICu and outperform other criteria, and for large sample sizes, WICu and WICs perform as well as BIC and SIC, respectively, and outperform other criteria.

Chapter 1 Introduction
1.1 Motivation
1.2 Overview
Chapter 2 Literature Review
2.1 Autoregressive Model
2.2 Order Selection Criteria
2.2.1 The AIC Criterion
2.2.2 The AICc Criterion
2.2.3 The AICu Criterion
2.2.4 The BIC Criterion
2.2.5 The SIC Criterion
2.2.6 The SICc Criterion
2.2.7 The ODQ Criterion
2.2.8 The WIC Criterion
2.3 Signal-to-Noise Ratios
Chapter 3 Methodology of Modified WIC
3.1 Derivation of WICu and WICs
3.2 Signal-to-Noise Ratios of WICu and WICs
Chapter 4 Simulation and Numerical Results
4.1 Simulations
4.2 Numerical Results of Signal-to-Noise Ratios
Chapter 5 Conclusion and Discussion
5.1 Conclusion
5.2 Future Study
References
Appendix A
Appendix B
Appendix C

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