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研究生： 謝心遠
Hsieh, Hsin-Yuan
論文名稱： 具有異質變異性之有限樣本線性迴歸模型穩健檢定
Finite-Sample Heteroskedasticity-Robust Tests for Linear Regression Models
指導教授： 林世昌
Lin, Eric S.
口試委員: 張焯然
Chang, Jow-Ran
林世昌
Lin, Eric S.
周大森
Chou, Ta-Sheng
學位類別： 碩士
Master
系所名稱： 科技管理學院 - 經濟學系
Department of Economics
論文出版年： 2020
畢業學年度： 108
語文別： 英文
論文頁數： 48
中文關鍵詞： 拔靴法 、有限樣本 、異質變異性 、局部檢定力 、半母數可行的一般化最小平方法 、顯著水準扭曲
外文關鍵詞： Bootstrap, Finite Sample, Heteroskedasticity, Local Power, Semiparametric FGLS, Size Distortion
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    • 異質變異性是迴歸分析中經常出現的議題。對於所有對異質變異性穩健的估計式而言，在適當的條件之下，一般化最小平方法（generalized least squares, GLS）估計式具備最高的有效性。另一方面，Hausman and Palmer （2011）提出了二階拔靴法（second-order bootstrap），並透過蒙地卡羅試驗展現其在小樣本中的優秀表現。然而，Richard （2017）透過更加廣泛的模擬發現二階拔靴法並沒有比wild bootstrap檢定更為穩健。據此，本文提出一個結合半母數可行的一般化最小平方法（semi-parametric feasible GLS）與wild bootstrap的檢定方法，輔以蒙地卡羅試驗評估其在小樣本當中的表現。經模擬後發現，當以無母數估計中的Nadaraya-Watson核估計（Nadaraya-Watson kernel estimator）或k近鄰估計（k-nearest neighbors estimator）與本文提出的方法搭配時，在多種資料型態當中「顯著水準扭曲（size distortion）」能夠被有效降低；同時在資料具備異質變異性的前提下，該估計法將比二階拔靴法具有更強的「局部檢定力（local power）」。

    Heteroskedasticity is an issue frequently occurs in the regression analysis. Among all the heteroskedasticity-robust estimators, the generalized least squares (GLS) estimator is the most efficient one under suitable conditions. On the other hand, Hausman and Palmer (2012) developed the second-order bootstrap (SOB) method and exhibited excellent finite-sample performance via simulation experiments. However, Richard (2017) examined the SOB method through more general simulations and discovered that it is not as robust as the wild bootstrap test. Accordingly, we propose an alternative testing procedure combining the semi-parametric feasible GLS estimator with the wild bootstrap test in this article. The proposed procedure's finite-sample performance is evaluated via a series of Monte Carlo experiments over a wide range of designs. The simulation results reveal that our proposed method based on the Nadaraya-Watson kernel estimator and the $k$-nearest neighbors estimator has noticeable effects in correcting size distortion in most circumstances, and gaining local power better than the SOB method when heteroskedasticity of unknown form exists.

    1 Introduction . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 1 2 The Heteroskedasticity-Robust Estimators and Tests . . . . . . . . . . . . . . . . . . 3 2.1 The Revised HCCMEs . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 4 2.2 The Bootstrap . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 6 2.3 The GLS Estimator . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 9 3 The Proposed Testing Procedure . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 10 3.1 The Nonparametric Skedastic Structure . . . . . . . . . . . . . . . . . . . . . . . . . . . 10 3.2 The Smoothing Parameters . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 12 3.3 Adding More Information to the Residuals . . . . . . . . . . . . . . . . . . . . . . . . . 12 3.4 The Testing Procedure . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 13 4 Simulation . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 14 4.1 Simulation Design . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 14 4.2 Advantages in terms of Choosing the Bootstrap Test with Restricted Residuals . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 16 4.2.1 Size Distortion . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 16 4.2.2 Local Power . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 22 4.3 Comparison with the Second-Order Bootstrap Method . . . . . . . . . . . . . . . 27 4.3.1 Size Distortion . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 27 4.3.2 Local Power . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 30 5 Conclusion . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 32 References . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 34 Appendix . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 38

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