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Value |
| Title: | 異質變異數矩陣之穩健估計 |
| Other Titles: | On Robust Estimation of the Heteroscedasticity Covariance Matrix |
| Authors: | 鄭宗記 |
| Contributors: | 國立政治大學統計學系
行政院國家科學委員會 |
| Keywords: | 異質變異;離群值;穩健估計
Heteroscedasticity;Outlier;Robust diagnostics |
| Date: | 2009 |
| Issue Date: | 2012-08-30 09:59:29 (UTC+8) |
| Abstract: | 迴歸模型分析的同質變異（homogenous variance）假設（即誤差之變異數為常數），在實 際資料分析中經常是不適當的。當模型中的誤差存在異質變異時，錯誤的標準誤的估計 將導致無效的統計推論。基於「異質變異一致性共變異數矩陣」（heteroscedasticity consistent covariance matrix，HCCM）估計的檢定方法，在應用上是廣為被使用 (White 1985) ，因其方法無須先明確異質變異的結構性為何。但離群值對於HCCM 的估計有相 當的影響(Cribari-Neto and Zarkos 2001; and Cribari-Neto 2004)，因此本計畫將討論異質 變異共變異數矩陣的穩健估計問題，其概念是應用Hubert and Rousseeuw (1997)所提出 之RDL1 穩健統計量，以及Giloni et al. (2006)的加權L1 估計方法。本研究將以模擬方 法針對所提出之穩健估計量的特性作詳細討論；同時將以實際資料分析來陳示該統計量 與傳統結果之差異。
The assumption of homogenous variance in the normal regression model is not always appropriate. The invalidity of standard inference procedure may be produced due to the wrong estimation of the standard error when the disturbance process in a regression model presents heteroscedasticity. Test based on a heteroscedasticity consistent covariance matrix (short for HCCM) estimator is popular in application because there is no need to specify the structural form of heteroscedasticity and it is easy to compute (White 1985). As several authors have reported that the leverage points are decisive for the finite sample behavior than the degree of heteroscedasticity in the estimation of HCCM (Cribari-Neto and Zarkos 2001; and Cribari-Neto 2004). In this project we propose a robust estimator for the heteroscedasticity covariance matrix, which is based on the concept of RDL1 estimator of Hubert and Rousseeuw (1997) and weighted L1 estimator of Giloni et al. (2006). Simulation studies are carried out to investigate the performance in terms of several configurations, such as sample size, dimension and proportion of outliers in the data. Furthermore, real data examples are used to illustrate the proposed method. |
| Relation: | 基礎研究
學術補助
研究期間:9808~ 9907
研究經費:580仟元 |
| Data Type: | report |
| DCField |
Value |
Language |
| dc.contributor (Contributor) | 國立政治大學統計學系 | en_US |
| dc.contributor (Contributor) | 行政院國家科學委員會 | en_US |
| dc.creator (Authors) | 鄭宗記 | zh_TW |
| dc.date (Date) | 2009 | en_US |
| dc.date.accessioned | 2012-08-30 09:59:29 (UTC+8) | - |
| dc.date.available | 2012-08-30 09:59:29 (UTC+8) | - |
| dc.date.issued (Issue Date) | 2012-08-30 09:59:29 (UTC+8) | - |
| dc.identifier.uri (URI) | http://nccur.lib.nccu.edu.tw/handle/140.119/53409 | - |
| dc.description.abstract (Abstract) | 迴歸模型分析的同質變異（homogenous variance）假設（即誤差之變異數為常數），在實 際資料分析中經常是不適當的。當模型中的誤差存在異質變異時，錯誤的標準誤的估計 將導致無效的統計推論。基於「異質變異一致性共變異數矩陣」（heteroscedasticity consistent covariance matrix，HCCM）估計的檢定方法，在應用上是廣為被使用 (White 1985) ，因其方法無須先明確異質變異的結構性為何。但離群值對於HCCM 的估計有相 當的影響(Cribari-Neto and Zarkos 2001; and Cribari-Neto 2004)，因此本計畫將討論異質 變異共變異數矩陣的穩健估計問題，其概念是應用Hubert and Rousseeuw (1997)所提出 之RDL1 穩健統計量，以及Giloni et al. (2006)的加權L1 估計方法。本研究將以模擬方 法針對所提出之穩健估計量的特性作詳細討論；同時將以實際資料分析來陳示該統計量 與傳統結果之差異。 | en_US |
| dc.description.abstract (Abstract) | The assumption of homogenous variance in the normal regression model is not always appropriate. The invalidity of standard inference procedure may be produced due to the wrong estimation of the standard error when the disturbance process in a regression model presents heteroscedasticity. Test based on a heteroscedasticity consistent covariance matrix (short for HCCM) estimator is popular in application because there is no need to specify the structural form of heteroscedasticity and it is easy to compute (White 1985). As several authors have reported that the leverage points are decisive for the finite sample behavior than the degree of heteroscedasticity in the estimation of HCCM (Cribari-Neto and Zarkos 2001; and Cribari-Neto 2004). In this project we propose a robust estimator for the heteroscedasticity covariance matrix, which is based on the concept of RDL1 estimator of Hubert and Rousseeuw (1997) and weighted L1 estimator of Giloni et al. (2006). Simulation studies are carried out to investigate the performance in terms of several configurations, such as sample size, dimension and proportion of outliers in the data. Furthermore, real data examples are used to illustrate the proposed method. | en_US |
| dc.language.iso | en_US | - |
| dc.relation (Relation) | 基礎研究 | en_US |
| dc.relation (Relation) | 學術補助 | en_US |
| dc.relation (Relation) | 研究期間:9808~ 9907 | en_US |
| dc.relation (Relation) | 研究經費:580仟元 | en_US |
| dc.subject (Keywords) | 異質變異;離群值;穩健估計 | en_US |
| dc.subject (Keywords) | Heteroscedasticity;Outlier;Robust diagnostics | en_US |
| dc.title (Title) | 異質變異數矩陣之穩健估計 | zh_TW |
| dc.title.alternative (Other Titles) | On Robust Estimation of the Heteroscedasticity Covariance Matrix | en_US |
| dc.type (Data Type) | report | en |
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