遷移學習在統計分析中扮演著日益重要的角色，尤其當資料可用性快速成長及需要整合多個來源資料的資訊時。雖然目前已有大量方法利用來源資料提升目標資料的估計效果，但仍有許多重要問題尚未探討。本論文旨在針對包含測量誤差與其他複雜特徵的資料，研發適用的遷移學習方法。
在第一章中，我們概述本論文，並回顧相關主題，包含複雜資料的統計模型、測量誤差模型與遷移學習及變數選取，並對每個主題進行文獻回顧。
卜瓦松迴歸模型已成為描述計數型應變數及共變數關係的常用方法。隨著資料收集的快速發展，獲取額外的來源資訊已變得更為容易。為了有效地應用來源資料改善原始資料的估計效果，遷移學習方法被認為是一種策略。然而，給定資料集面臨的挑戰包括測量誤差和變數的高維度。在第二章中，我們提出了一種新的策略來處理具有測量誤差的計數型應變數，並使用來源資料估計測量誤差模型中的參數，然後採用遷移學習方法導出不偏估計量。此外，為了提高預測精準度並避免模型不確定性，我們進一步建立了模型平均策略。模擬和乳癌資料研究驗證了所提出方法的良好表現且能有效處理測量誤差的問題。
在第三章中，我們研究了含有測量誤差共變數的無母數廣義相加模型（GAMs），並提出了一種新的基於測量誤差校正迴歸樹的遷移學習方法，以同時偵測資訊豐富的來源資料、變數選取和測量誤差校正的問題。同時，我們開發了方法偵測資訊豐富的來源資料及估計測量誤差模型中的未知變異數。模擬結果顯示，本文方法於非線性關係下，在預測精準度和變數選取方面均優於現有方法。將此方法應用於世界衛生組織全球衛生觀察站的真實死亡率資料，驗證了其實用性。
在第四章中，我們分析了事件發生時間資料，並針對具有測量誤差共變數的加速失效模型提出了遷移學習方法。其中的挑戰包括：因設限而產生的不完整應變數、高維度設定中無關變數，以及資料收集過程中引入的測量誤差。為了同時解決多個資料集分析中的這些挑戰，我們採用了遷移學習方法，並結合了模擬外推法（SIMEX）及梯度提升演算法，從而有效地進行變數選取及校正測量誤差。我們進一步開發了一種基於交叉驗證的策略，用於偵測資訊豐富的來源資料集，並在不依賴輔助資訊的情況下估計測量誤差的變異數。所提出的方法適用於多種設限機制。大量的模擬研究以及對浸潤性小葉癌資料的實際應用，證實了本方法的有效性與優異的實證表現。
最後，第五章總結了本論文，並討論了相關內容，同時展望未來的研究方向。

Transfer learning plays an increasingly important role in statistical analysis, particularly with the rapid growth of data availability and the need to integrate information from multiple sources. While a large body of methods have been developed to leverage source data to improve estimation for target data, many important problems remain underexplored. In this dissertation, we focus on the development of transfer learning methods for data with measurement error and other complex features.

In Chapter 1, we provide an introduction to the dissertation and review relevant topics including statistical models for complex data, measurement error models, and transfer learning and variable selection, and literature review for each topic.

Poisson regression model has been a popular approach to characterize the count response and the covariates. With the rapid development of data collections, the additional source information can be easily recorded. To efficiently use the source data to improve the estimation under the original data, the transfer learning method is considered a strategy. However, challenging issues from the given datasets include measurement error and high-dimensionality in variables. In Chapter 2, we propose a novel strategy to handle error-prone count responses and estimate the parameters in measurement error models by using the source data, and then employ the transfer learning method to derive the debiased estimator. Moreover, to improve the prediction and avoid the model uncertainty, we further establish the model averaging strategy. Simulation and breast cancer data studies verify the satisfactory performance of the proposed method and the validity of handling measurement error.

In Chapter 3, we study nonparametric generalized additive models (GAMs) with noisy covariates and propose a novel error-corrected regression tree-based transfer learning method to address informative source detection, variable selection, and error correction simultaneously. Meanwhile, we develop valid strategies for source data detection and estimation of unknown variances in measurement error models. Simulation results demonstrate that our method achieves superior performance in both prediction accuracy and variable selection compared to existing approaches, particularly under nonlinear relationships. An application to real-world mortality data from the WHO Global Health Observatory confirms the practical utility of our method.

In Chapter 4, we analyze the time-to-event data and propose transfer learning for accelerated failure time models with noisy covariates, where the challenges include incomplete outcomes arising from censoring, the presence of irrelevant variables in high-dimensional settings, and measurement error introduced during data collection. To simultaneously address these challenges in the analysis of multiple datasets, we adopt the transfer learning method by incorporating the simulation and extrapolation (SIMEX) approach and the boosting algorithm, which together enable effective variable selection and correction for measurement error. We further develop a cross-validation-based strategy to identify informative source datasets and to estimate the measurement error variance without relying on auxiliary information. The proposed method is applicable to a broad class of censoring mechanisms. Extensive simulation studies and an application to invasive lobular carcinoma data demonstrate the validity and strong empirical performance of the proposed approach.

Finally, Chapter 5 summarizes the dissertation with discussions and outlines future research.

Anderson-Bergman, C. (2017). icenReg: Regression models for interval censored data in R. Journal of Statistical Software, 81, 1–23.
Arpino, G., Bardou, V. J., Clark, G. M., and Elledge, R. M. (2004). Infiltrating lobular carcinoma of the breast: Tumor characteristics and clinical outcome. Breast Cancer Research, 6, R149.
Aydin, D., Yilmaz, E., Chamidah, N., Lestari, B., and Budiantara, I. N. (2025). Right-censored nonparametric regression with measurement error. Metrika, 88, 183–214.
Barnwal, A., Cho, H., and Hocking, T. (2022). Survival regression with accelerated failure time model in XGBoost. Journal of Computational and Graphical Statistics, 31, 1292–1302.
Baslan, T., Kendall, J., Volyanskyy, K., McNamara, K., Cox, H., D’Italia, S., Ambrosio, F., Riggs, M., Rodgers, L., Leotta, A., Song, J., Mao, Y., Wu, J., Shah, R., Gularte-Mérida, R., Chadalavada, K., Nanjangud, G., Varadan, V., Gordon, A., ...Hicks, J. (2020). Novel insights into breast cancer copy number genetic heterogeneity revealed by single-cell genome sequencing. eLife, 9, e51480.
Bastani, H. (2021). Predicting with proxies: Transfer learning in high dimension. Management Science, 67, 2964–2984.
Boyd, S. and Vandenberghe, L. (2004). Convex Optimization. Cambridge University Press, Cambridge.
Breiman, L., Friedman, J., Olshen, R. A., and Stone, C. J. (1984). Classification and Regression Trees. Chapman and Hall/CRC, Boca Raton.
Buckley, J. and James, I. (1979). Linear regression with censored data. Biometrika, 66, 429–436.
Bühlmann, P. and Yu, B. (2003). Boosting with the L2 loss: Regression and classification. Journal of the American Statistical Association, 98, 324–339.
Cai, T. T. and Pu, H. (2024). Transfer learning for nonparametric regression: Non-asymptotic minimax analysis and adaptive procedure. arXiv preprint. https://arxiv.org/abs/2401. 12272
Carroll, R. J., Ruppert, D., Stefanski, L. A., and Crainiceanu, C. M. (2006). Measurement Error in Nonlinear Models: A Modern Perspective. Chapman and Hall/CRC, Boca Raton.
Chen, A., Owen, A. B., and Shi, M. (2015). Data enriched linear regression. Electronic Journal of Statistics, 9, 1078–1112.
Chen, B., Yuan, A., and Yi, G. Y. (2021). Variable selection for proportional hazards models with high-dimensional covariates subject to measurement error. The Canadian Journal of Statistics, 49, 397–420.
Chen, L.-P. (2023). De-noising boosting methods for variable selection and estimation subject to error-prone variables. Statistics and Computing, 33, 38.
Chen, L.-P. and Huang, H.-T. (2024). AFFECT: An R package for accelerated functional failure time model with error-contaminated survival times and applications to gene expression data. BMC Bioinformatics, 25, 265.
Chen, L.-P. and Qiu, B. (2023a). Analysis of length-biased and partly interval-censored survival data with mismeasured covariates. Biometrics, 79, 3929–3940.
Chen, L.-P. and Qiu, B. (2023b). SIMEXBoost: An R package for analysis of high-dimensional error-prone data based on boosting method. The R Journal, 15, 5–20.
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) 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 Yi, G. Y. (2021b). Analysis of noisy survival data with graphical proportional hazards measurement error models. Biometrics, 77, 956–969.
Chen, X., Ji, H., Luan, Y., Zoh, R. S., Xue, L., Jadhav, S., and Tekwe, C. D. (2024). Adjusting for bias due to measurement error in functional quantile regression models with error-prone functional and scalar covariates. Biostatistics and Epidemiology, 8, 1–20.
Chiang, D. Y., Getz, G., Jaffe, D. B., O’Kelly, M. J., Zhao, X., Carter, S. L., Russ, C., Nusbaum, C., Meyerson, M., and Lander, E. S. (2009). High-resolution mapping of copy-number alterations with massively parallel sequencing. Nature Methods, 6, 99–103.
Chiou, S. H., Kang, S., and Yan, J. (2014). Fitting accelerated failure time models in routine survival analysis with R. Journal of Statistical Software, 61, 1–23.
Davidson, C. D., Gillis, N. E., and Carr, F. E. (2021). Thyroid hormone receptor beta as tumor suppressor: untapped potential in treatment and diagnostics in solid tumors. Cancers (Basel), 13, 4254.
Friedman, J. H. (2001). Greedy function approximation: A gradient boosting machine. The Annals of Statistics, 29, 1189–1232.
Friedman, J. H., Hastie, T., and Tibshirani, R. (2010). Regularization paths for generalized linear models via coordinate descent. Journal of Statistical Software, 33, 1–22.
Gao, F., Zeng, D., and Lin, D. Y. (2017). Semiparametric estimation of the accelerated failure time model with partly interval-censored data. Biometrics, 73, 1161–1168.
García-Zattera, M. J., Jara, A., and Komárek, A. (2016). A flexible AFT model for misclassified clustered interval-censored data. Biometrics, 72, 473–483.
Grasso, C., Butler, T., Rhodes, K., Quist, M., Neff, T. L., Moore, S., Tomlins, S. A., Reinig, E., Beadling, C., Andersen, M., and Corless, C. L. (2015). Assessing copy number alterations in targeted, amplicon-based next-generation sequencing data. The Journal of Molecular Diagnostics, 17, 53–63.
Harrell, F. E. (2015). Regression Modeling Strategies: With Applications to Linear Models, Logistic and Ordinal Regression, and Survival Analysis. (2nd ed.). Springer, Cham.
Hastie, T. and Tibshirani, R. (1986). Generalized additive models. Statistical Science, 1, 297– 310.
Hothorn, T., Bühlmann, P., Kneib, T., Schmid, M., Hofner, B. (2010). Model-based boosting 2.0. Journal of Machine Learning Research, 11, 2109–2113.
Jiang, F., Zhou, Y., Liu, J., and Ma, Y. (2023). On high-dimensional Poisson models with measurement error: hypothesis testing for nonlinear nonconvex optimization. The Annals of Statistics, 51, 233–259.
Kalbfleisch, J. D. and Prentice, R. L. (2011). The Statistical Analysis of Failure Time Data. Wiley, New Jersey.
Klosa, J., Simon, N., Westermark, P. O., Liebscher, V., and Wittenburg, D. (2020). Seagull: Lasso, group lasso and sparse-group lasso regularization for linear regression models via proximal gradient descent. Bioinformatics, 21, 407.
Kukush, A., Schneeweis, H., and Wolf, R. (2004). Three estimators for the Poisson regression model with measurement errors. Statistical Papers, 45, 351–368.
Lagani, V. and Tsamardinos, I. (2010). Structure-based variable selection for survival data. Bioinformatics, 26, 1887–1894.
Lange, K. (2001). Numerical Analysis for Statisticians. Springer, New York.
Lawless, J. F. (2003). Statistical Models and Methods for Lifetime Data. John Wiley & Sons, New Jersey.
Lee, E. R., Han, K., and Park, B. U. (2018). Estimation of errors-in-variables partially linear
additive models. Statistica Sinica, 28, 2353–2373.
Lee, S., Kwon, S., and Kim, Y. (2016). A modified local quadratic approximation algorithm for penalized optimization problems. Computational Statistics and Data Analysis, 94, 275–286.
Li, J. and Ma, J. (2020). On hazard-based penalized likelihood estimation of accelerated failure time model with partly interval censoring. Statistical Methods in Medical Research, 29, 3804–3817.
Li, S., Cai, T. T., and Li, H. (2022). Transfer learning for high-dimensional linear regression: Prediction, estimation and minimax optimality. Journal of the Royal Statistical Society Series B: Statistical Methodology, 84, 149–173.
Li, Y. and Ryan, L. (2004). Survival analysis with heterogeneous covariate measurement error. Journal of the American Statistical Association, 99, 724–735.
Li, Z., Shen, Y., and Ning, J. (2023). Accommodating time-varying heterogeneity in risk estimation under the Cox model: A transfer learning approach. Journal of the American Statistical Association, 118, 2276–2287.
Lin, L. and Li, W. (2023). Source-function weighted transfer learning for nonparametric regression. arXiv preprint. https://arxiv.org/abs/2302.11222
Liu, H., Men, J., Wang, S., You, J., and Cao, J. (2025). Similarity-informed transfer learning for multivariate functional censored quantile regression. arXiv preprint. https://arxiv.org/ abs/2503.18437
Liu, M., Zhang, Y., Liao, K. P., and Cai, T. (2023). Augmented transfer regression learning with semi-nonparametric nuisance models. Journal of Machine Learning Research, 24, 1–50.
Liu, R. Z., Garcia, E., Glubrecht, D. D., Poon, H. Y., Mackey, J. R., and Godbout, R. (2015). CRABP1 is associated with a poor prognosis in breast cancer: Adding to the complexity of breast cancer cell response to retinoic acid. Molecular Cancer, 14, 129.
Lovejoy, C. A., Xu, X., Bansbach, C. E., Glick, G. G., Zhao, R., Ye, F., Sirbu, B. M., Titus, L. C., Shyr, Y., and Cortez, D. (2009). Functional genomic screens identify CINP as a genome maintenance protein. Proceedings of the National Academy of Sciences, 106, 19304–19309.
Ma, S. (2006). Empirical study of supervised gene screening. BMC Bioinformatics, 7, 537.
Molstad, A. J. and Suder, P. M. (2025). penAFT: Fit the semiparametric accelerated failure time models with elastic net and sparse group lasso penalties. R package version 0.3.2, https://CRAN.R-project.org/package=penAFT
Nakamura, T. (1992). Proportional hazards model with covariates subject to measurement error. Biometrics, 48, 829–838.
Olivier, M., Hollstein, M., and Hainaut, P. (2010). TP53 mutations in human cancers: origins, consequences, and clinical use. Cold Spring Harbor Perspectives in Biology, 2, a001008.
Pei, Y. B., Yu, Z. Y., and Shen, J. S. (2025). Transfer learning for accelerated failure time model with microarray data. BMC Bioinformatics, 26, 1–19.
Pestalozzi, B. C., Zahrieh, D., Mallon, E., Gusterson, B. A., Price, K. N., Gelber, R. D., Holm- berg, S. B., Lindtner, J., Snyder, R., Thürlimann, B., Murray, E., Viale, G., Castiglione- Gertsch, M., Coates, A. S., and Goldhirsch, A. (2008). Distinct clinical and prognostic features of infiltrating lobular carcinoma of the breast: Combined results of 15 international breast cancer study group clinical trials. Journal of Clinical Oncology, 26, 3006–3014.
Ravikumar, P., Lafferty, J., Liu, H., and Wasserman, L. (2009). Sparse additive models. Journal of the Royal Statistical Society Series B: Statistical Methodology, 71, 1009–1030.
Sexton, J. and Laake, P. (2007). Regression trees with errors in variables. Biometrics, 63, 586– 592.
Smith, P. J. (2002). Analysis of Failure and Survival Data. Chapman and Hall/CRC, Boca Raton.
Sørensen, Ø., Hellton, K. H., Frigessi, A., and Thoresen, M. (2018). Covariate selection in high-dimensional generalized linear models with measurement error. Journal of Computational and Graphical Statistics, 27, 739–749.
Stoklosa, J., Hwang, W.-H., and Warton, D. I. (2023). A general algorithm for error-in-variables regression modelling using Monte Carlo expectation maximization. PLOS ONE, 18, e0283798.
Sun, T. and Ding, Y. (2023). Neural network on interval-censored data with application to the prediction of Alzheimer’s disease. Biometrics, 79, 2677–2690.
Therneau, T. M. (2024). survival: A package for survival analysis in R. R package version 3.8-3, https://CRAN.R-project.org/package=survival
Tian, Y. and Feng, Y. (2023). Transfer learning under high-dimensional generalized linear models. Journal of the American Statistical Association, 118, 2684–2697.
Tsai, L.-J., Hsiao, S.-H., Tsai, L.-M., Lin, C.-Y., Tsai, J.-J., Liou, D.-M., and Lan, J.-L. (2008). The sodium-dependent glucose cotransporter SLC5A11 as an autoimmune modifier gene in SLE. Tissue Antigens, 71, 114–126.
Tu, Y., Stolovitzky, G., and Klein, U. (2002). Quantitative noise analysis for gene expression microarray experiments. Proceedings of the National Academy of Sciences, 99, 14031–14036.
Turner, N., Pearson, A., Sharpe, R., Lambros, M., Geyer, F., Lopez-Garcia, M. A., Natrajan, R., Marchio, C., Iorns, E., Mackay, A., Gillett, C., Grigoriadis, A., Tutt, A., Reis-Filho, J. S., and Ashworth, A. (2010). FGFR1 amplification drives endocrine therapy resistance and is a therapeutic target in breast cancer. Cancer Research, 70, 2085–2094.
Wang, F. and Yu, Y. (2025). Transfer learning for piecewise-constant mean estimation: Optimality, l1- and l0-penalization. Biometrika, 112, asaf018.
Wang, P., Weng, J., and R. G. W. Anderson. (2005). OSBP is a cholesterol-regulated scaffolding protein in control of ERK1/2 activation. Science, 307, 1472–1476.
Wang, Z. (2023). bujar: Buckley-James regression for survival data with high-dimensional covariates. R package version 0.2-11, https://CRAN.R-project.org/package=bujar
Wolfson, J. (2011). EEBoost: A general method for prediction and variable selection based on estimating equations. Journal of the American Statistical Association, 106, 296–305.
Wood, S. N. (2017). Generalized Additive Models: An Introduction with R. Chapman and Hall/CRC, Boca Raton.
World Health Organization. (n.d.). Global Health Observatory (GHO) data: Indicators index. World Health Organization. Retrieved April 29, 2025, from https://www.who.int/data/ gho/data/indicators/indicators-index
World Health Organization. (2020). Global Health Estimates Technical Paper WHO/DDI/DNA /GHE/2020.1: Methods for estimating the burden of disease attributable to selected risk factors. World Health Organization.
Wu, J.-C. and Chen, L.-P. (2025). Transfer learning for error-contaminated Poisson regression models. Statistics in Medicine, 44, e70163.
Xie, M., Hu, T., and Zhou, J. (2024). Transfer learning under the Cox model with interval-censored data. Statistical Analysis and Data Mining: The ASA Data Science Journal, 17, e11680.
Yang, H., Pan, F., Tong, D., Brown, H. E., and Liu, J. (2024). Measurement error-tolerant Poisson regression for Valley Fever incidence prediction. IISE Transactions on Healthcare Systems Engineering, 14, 305–317.
Yi, G. Y. (2017). Statistical Analysis with Measurement Error or Misclassification. Springer-
Verlag New York.
Zhang, L. and Zhang, L. (2013). Use of autocorrelation scanning in DNA copy number analysis. Bioinformatics, 29, 2678–2682.
Zhang, Q. and Yi, G. Y. (2023). Zero-inflated Poisson models with measurement error in the response. Biometrics, 79, 1089–1102.
Zhang, X., Ma, Y., and Carroll, R. J. (2019). MALMEM: model averaging in linear measurement error models. Journal of the Royal Statistical Society Series B: Statistical Methodology, 81, 763–779.
Zhao, P., Josse, J., and Yang, S. (2025). Efficient and robust transfer learning of optimal individualized treatment regimes with right-censored survival data. Journal of Machine Learning Research, 26, 1–54.
Zou, J., Wang, W., Zhang, X., and Zou, G. (2022). Optimal model averaging for divergent- dimensional Poisson regressions. Econometric Reviews, 41, 775–805.