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題名 帶有錯誤分類與測量誤差數據的高維度變數選取與估計
Variable selection and estimation for misclassified responses and high-dimensional error-prone predictors作者 歐陽沁縈
Ou Yang, Qin-Ying貢獻者 陳立榜
Chen, Li-Pang
歐陽沁縈
Ou Yang, Qin-Ying關鍵詞 二元分類資料
boosting
誤差校正
測量誤差
回歸模型校正
binary data
boosting
error elimination
measurement error
regression calibration日期 2022 上傳時間 1-Aug-2022 17:15:25 (UTC+8) 摘要 二元分類一直是統計分析或監督式學習中值得被討論的內容。在建立二元結果與變數的模型選擇上,logistic 與 probit 的模型是較常被使用的。然而,在資料維度遽增以及不可忽視的測量誤差存在測量結果、變數當中,過去的傳統方法已不適用,這為我們在資料分析上帶來了重大的挑戰。為了解決上述的問題,我們提出有效的推論方法處理測量誤差並同時進行變數選取。具體來說,我們首先考慮 logistic 或 probit 的模型,將經過校正的應變數與自變數放入我們的估計函數中。接著,我們透過 boosting 方法去做變數選取並計算參數的估計值。在數值研究當中,我們所提出的方法能夠準確地保留重要變數且能精準地計算出估計參數。此外,經過誤差校正的結果在整體的分析表現上是顯著優於沒有校正的結果。
Binary classification has been an attractive topic in statistical analysis or supervised learning. To model a binary response and predictors, logistic regression models or probit models are perhaps commonly used approaches. However, because of the rapid growth of the dimension of the data as well as the non ignorability of measurement error in responses and/or predictors, data analysis becomes challenging and conventional methods are invalid. To address those concerns, we propose a valid inferential method to deal with measurement error and handle variable selection simultaneously. Specifically, we primarily consider logistic regression models or probit models, and propose corrected estimating functions by incorporating error-eliminated responses and predictors. After that, we develop the boosting procedure with corrected estimating functions accommodated to do variable selection and estimation.Through numerical studies, we find that the proposed method accurately retains informative predictors as well as gives precise estimators, and its performance is generally better than that without measurement error correction.參考文獻 Brown, B., Miller, C. J., and Wolfson, J. (2017). ThrEEBoost: Thresholded boosting for variable selection and prediction via estimating equations. Journal of Computational and Graphical Statistics, 26, 579-588.Brown, B., Weaver, T., and Wolfson, J. (2019). MEBoost: Variable selection in the presence of measurement error. Statistics in Medicine, 38, 2705-2718.Carroll, R. J., Ruppert, D., Stefanski, L. A., and Crainiceanu, C. M. (2006). Measurement Error in Nonlinear Model. Chapman and Hall.Carroll, R. J., Spiegelman, C. H., Gordon Lan, K. K., Bailey, K. T., and Abbott, R. D. (1984). On errors-in-variables for binary regression models. Biometrika, 71, 19-25.Chen, L.-P. (2020). Variable selection and estimation for the additive hazards model subject to left-truncation, right-censoring and measurement error in covariates. Journal of Statistical Computation and Simulation, 90, 3261-3300.Chen, L.-P. and Yi, G. Y. (2020). Model selection and model averaging for analysis of truncated and censored data with measurement error. Electronic Journal of Statistics, 14, 4054–4109.Chen, L.-P. and Yi, G. Y. (2021a). Analysis of noisy survival data with graphical proportional hazards measurement error models. Biometrics, 77, 956–969.Chen, L.-P. and Yi, G. Y. (2021b). Semiparametric methods for left-truncated and right-censored survival data with covariate measurement error. Annals of the Institute of Statistical Mathematics, 73, 481–517.Chen, L.-P. and Yang, S.-F. (2022). A new p-chart with measurement error correction. arXiv:2203.03384.Hastie, T., Tibshironi, R., and Wainwright, M. (2015). Statistical Learning with Sparsity: The Lasso and Generalization. CRC Press, Boca Raton, FL.Laitinen, E. K., and Laitinen, T. (1997). Misclassification in bankruptcy prediction in Finland: human information processing approach. Accounting, Auditing & Accountability Journal, 11, 216-244.Liang, D., Lu, C. C., Tsai, C. F., and Shih, G. A. (2016). Financial ratios and corporate governance indicators in bankruptcy prediction: A comprehensive study. European Journal of Operational Research, 16, 561-572.Ma, Y. and Li, R. (2010). Variable selection in measurement error models. Bernoulli, 16, 273-300.Marquardt, D. W. and Snee, R. D. (1975). Ridge regression in practice. The American Statistician, 29, 3-20.McGlothlin, A., Stamey, J. D., and Seaman, J. W. (2008). Binary regression with misclassified response and covariate subject to measurement error: a bayesian approach. Biometrika, 50, 123-134.Nanda, S. and Pendharkar, P. (2001). Linear models for minimizing misclassification costs in bankruptcy prediction. International Journal of Intelligent Systems in Accounting, Finance & Management, 10, 155–168.Reeves, G. K., Cox, D. R., Darry, S. C., and Whitley, E. (1998). Some aspects of measurement error in explanatory variables for continuous and binary regression models. Statistics in Medicine, 17, 2157-2177.Roy, S., Banerjee, T., and Maiti, T. (2005). Measurement error model for misclassified binary responses. Statistics in Medicine, 24, 269-283.Schafer, D. W. (1993). Analysis for probit regression with measurement errors. Biometrika, 80, 899-904.Shao, J. (2003). Mathematical Statistics. Springer, New York.Sørensen, Ø., Frigessi, A., and Thoresen, M. (2015). Measurement error in lasso: impact and likelihood bias correction. Statistica Sinica, 25, 809-829.Stefanski, L. A. and Carroll, R. J. (1987). Conditional scores and optimal scores for generalized linear measurement error models. Biometrika, 74, 703-716.Wolfson, J. (2011). EEBOOST: a general method for prediction and variable selection based on estimating equation. Journal of the American Statistical Association, 106, 296-305.Yi, G. Y. (2017). Statistical Analysis With Measurement Error and Misclassication: Strategy, Method and Application. New York: Springer.Zhang, T. and Yu, B. (2005). Boosting with early stopping: convergence and consistency. The Annals of Statistics , 33, 1538-1579.Zou, H. and Hastie, T. (2005). Regularization and variable selection via the elastic net. Journal of the Royal Statistical Society, Series B, 67, 301-320. 描述 碩士
國立政治大學
統計學系
109354014資料來源 http://thesis.lib.nccu.edu.tw/record/#G0109354014 資料類型 thesis dc.contributor.advisor 陳立榜 zh_TW dc.contributor.advisor Chen, Li-Pang en_US dc.contributor.author (Authors) 歐陽沁縈 zh_TW dc.contributor.author (Authors) Ou Yang, Qin-Ying en_US dc.creator (作者) 歐陽沁縈 zh_TW dc.creator (作者) Ou Yang, Qin-Ying en_US dc.date (日期) 2022 en_US dc.date.accessioned 1-Aug-2022 17:15:25 (UTC+8) - dc.date.available 1-Aug-2022 17:15:25 (UTC+8) - dc.date.issued (上傳時間) 1-Aug-2022 17:15:25 (UTC+8) - dc.identifier (Other Identifiers) G0109354014 en_US dc.identifier.uri (URI) http://nccur.lib.nccu.edu.tw/handle/140.119/141006 - dc.description (描述) 碩士 zh_TW dc.description (描述) 國立政治大學 zh_TW dc.description (描述) 統計學系 zh_TW dc.description (描述) 109354014 zh_TW dc.description.abstract (摘要) 二元分類一直是統計分析或監督式學習中值得被討論的內容。在建立二元結果與變數的模型選擇上,logistic 與 probit 的模型是較常被使用的。然而,在資料維度遽增以及不可忽視的測量誤差存在測量結果、變數當中,過去的傳統方法已不適用,這為我們在資料分析上帶來了重大的挑戰。為了解決上述的問題,我們提出有效的推論方法處理測量誤差並同時進行變數選取。具體來說,我們首先考慮 logistic 或 probit 的模型,將經過校正的應變數與自變數放入我們的估計函數中。接著,我們透過 boosting 方法去做變數選取並計算參數的估計值。在數值研究當中,我們所提出的方法能夠準確地保留重要變數且能精準地計算出估計參數。此外,經過誤差校正的結果在整體的分析表現上是顯著優於沒有校正的結果。 zh_TW dc.description.abstract (摘要) Binary classification has been an attractive topic in statistical analysis or supervised learning. To model a binary response and predictors, logistic regression models or probit models are perhaps commonly used approaches. However, because of the rapid growth of the dimension of the data as well as the non ignorability of measurement error in responses and/or predictors, data analysis becomes challenging and conventional methods are invalid. To address those concerns, we propose a valid inferential method to deal with measurement error and handle variable selection simultaneously. Specifically, we primarily consider logistic regression models or probit models, and propose corrected estimating functions by incorporating error-eliminated responses and predictors. After that, we develop the boosting procedure with corrected estimating functions accommodated to do variable selection and estimation.Through numerical studies, we find that the proposed method accurately retains informative predictors as well as gives precise estimators, and its performance is generally better than that without measurement error correction. en_US dc.description.tableofcontents Chapter 1 Introduction 1Chapter 2 Notation and Models 32.1 Data Structure 32.2 Measurement Error Models 4Chapter 3 Methodology 63.1 Correction of Measurement Error Effects 63.2 Variable Selection via Boosting 83.3 Extension: Collinearity 11Chapter 4 Estimation with Validation Data 114.1 BOOME via External Validation 124.2 BOOME via Internal Validation 13Chapter 5 Python Package: BOOME 145.1 ME_Generate 145.2 LR_Boost 155.3 PM_Boost 16Chapter 6 Numerical Studies 166.1 Simulation Setup 166.2 Simulation Results 176.3 Simulation Results based on Validation Data 196.4 Analysis of Bankruptcy Data 19Chapter 7 Summary 21References 23Appendix 26A.1 Proof of Theorem 3.1 26A.2 Proof of Theorem 3.2 28A.3 Proof of Theorem 3.3 29 zh_TW dc.format.extent 1511038 bytes - dc.format.mimetype application/pdf - dc.source.uri (資料來源) http://thesis.lib.nccu.edu.tw/record/#G0109354014 en_US dc.subject (關鍵詞) 二元分類資料 zh_TW dc.subject (關鍵詞) boosting zh_TW dc.subject (關鍵詞) 誤差校正 zh_TW dc.subject (關鍵詞) 測量誤差 zh_TW dc.subject (關鍵詞) 回歸模型校正 zh_TW dc.subject (關鍵詞) binary data en_US dc.subject (關鍵詞) boosting en_US dc.subject (關鍵詞) error elimination en_US dc.subject (關鍵詞) measurement error en_US dc.subject (關鍵詞) regression calibration en_US dc.title (題名) 帶有錯誤分類與測量誤差數據的高維度變數選取與估計 zh_TW dc.title (題名) Variable selection and estimation for misclassified responses and high-dimensional error-prone predictors en_US dc.type (資料類型) thesis en_US dc.relation.reference (參考文獻) Brown, B., Miller, C. J., and Wolfson, J. (2017). ThrEEBoost: Thresholded boosting for variable selection and prediction via estimating equations. Journal of Computational and Graphical Statistics, 26, 579-588.Brown, B., Weaver, T., and Wolfson, J. (2019). MEBoost: Variable selection in the presence of measurement error. Statistics in Medicine, 38, 2705-2718.Carroll, R. J., Ruppert, D., Stefanski, L. A., and Crainiceanu, C. M. (2006). Measurement Error in Nonlinear Model. Chapman and Hall.Carroll, R. J., Spiegelman, C. H., Gordon Lan, K. K., Bailey, K. T., and Abbott, R. D. (1984). On errors-in-variables for binary regression models. Biometrika, 71, 19-25.Chen, L.-P. (2020). Variable selection and estimation for the additive hazards model subject to left-truncation, right-censoring and measurement error in covariates. Journal of Statistical Computation and Simulation, 90, 3261-3300.Chen, L.-P. and Yi, G. Y. (2020). Model selection and model averaging for analysis of truncated and censored data with measurement error. Electronic Journal of Statistics, 14, 4054–4109.Chen, L.-P. and Yi, G. Y. (2021a). Analysis of noisy survival data with graphical proportional hazards measurement error models. Biometrics, 77, 956–969.Chen, L.-P. and Yi, G. Y. (2021b). Semiparametric methods for left-truncated and right-censored survival data with covariate measurement error. Annals of the Institute of Statistical Mathematics, 73, 481–517.Chen, L.-P. and Yang, S.-F. (2022). A new p-chart with measurement error correction. arXiv:2203.03384.Hastie, T., Tibshironi, R., and Wainwright, M. (2015). Statistical Learning with Sparsity: The Lasso and Generalization. CRC Press, Boca Raton, FL.Laitinen, E. K., and Laitinen, T. (1997). Misclassification in bankruptcy prediction in Finland: human information processing approach. Accounting, Auditing & Accountability Journal, 11, 216-244.Liang, D., Lu, C. C., Tsai, C. F., and Shih, G. A. (2016). Financial ratios and corporate governance indicators in bankruptcy prediction: A comprehensive study. European Journal of Operational Research, 16, 561-572.Ma, Y. and Li, R. (2010). Variable selection in measurement error models. Bernoulli, 16, 273-300.Marquardt, D. W. and Snee, R. D. (1975). Ridge regression in practice. The American Statistician, 29, 3-20.McGlothlin, A., Stamey, J. D., and Seaman, J. W. (2008). Binary regression with misclassified response and covariate subject to measurement error: a bayesian approach. Biometrika, 50, 123-134.Nanda, S. and Pendharkar, P. (2001). Linear models for minimizing misclassification costs in bankruptcy prediction. International Journal of Intelligent Systems in Accounting, Finance & Management, 10, 155–168.Reeves, G. K., Cox, D. R., Darry, S. C., and Whitley, E. (1998). Some aspects of measurement error in explanatory variables for continuous and binary regression models. Statistics in Medicine, 17, 2157-2177.Roy, S., Banerjee, T., and Maiti, T. (2005). Measurement error model for misclassified binary responses. Statistics in Medicine, 24, 269-283.Schafer, D. W. (1993). Analysis for probit regression with measurement errors. Biometrika, 80, 899-904.Shao, J. (2003). Mathematical Statistics. Springer, New York.Sørensen, Ø., Frigessi, A., and Thoresen, M. (2015). Measurement error in lasso: impact and likelihood bias correction. Statistica Sinica, 25, 809-829.Stefanski, L. A. and Carroll, R. J. (1987). Conditional scores and optimal scores for generalized linear measurement error models. Biometrika, 74, 703-716.Wolfson, J. (2011). EEBOOST: a general method for prediction and variable selection based on estimating equation. Journal of the American Statistical Association, 106, 296-305.Yi, G. Y. (2017). Statistical Analysis With Measurement Error and Misclassication: Strategy, Method and Application. New York: Springer.Zhang, T. and Yu, B. (2005). Boosting with early stopping: convergence and consistency. The Annals of Statistics , 33, 1538-1579.Zou, H. and Hastie, T. (2005). Regularization and variable selection via the elastic net. Journal of the Royal Statistical Society, Series B, 67, 301-320. zh_TW dc.identifier.doi (DOI) 10.6814/NCCU202200889 en_US
