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For efficient estimation of model parameters, we develop a sieve maximum likelihood approach where parametric and nonparametric coefficients are bundled with an unknown baseline hazard function in the likelihood function. Not only do the bundled parameters cause immense numerical difficulties, but they also result in new challenges in theoretical development. By developing a general theoretical framework, we overcome the challenges arising from the bundled parameters and derive the convergence rate of the proposed estimator. Additionally, we prove that the finite-dimensional estimator is root-$ {n} $ consistent, asymptotically normal and achieves the semiparametric information bound. Furthermore, we demonstrate the nonparametric optimality of the functional estimator and construct the asymptotic simultaneous confidence band. The proposed inference procedures are evaluated by extensive simulation studies and illustrated with an application to the National Health and Nutrition Examination Survey data.<\/jats:p>","DOI":"10.1093\/biomet\/asaf011","type":"journal-article","created":{"date-parts":[[2025,3,7]],"date-time":"2025-03-07T19:22:32Z","timestamp":1741375352000},"source":"Crossref","is-referenced-by-count":1,"title":["Efficient estimation for functional accelerated failure time models"],"prefix":"10.1093","volume":"112","author":[{"ORCID":"https:\/\/orcid.org\/0000-0002-8185-0191","authenticated-orcid":false,"given":"Changyu","family":"Liu","sequence":"first","affiliation":[{"name":"Department of Statistics, The Chinese University of Hong Kong , Shatin, New Territories, Hong Kong"}],"role":[{"role":"author","vocabulary":"crossref"}]},{"ORCID":"https:\/\/orcid.org\/0000-0002-4597-4541","authenticated-orcid":false,"given":"Wen","family":"Su","sequence":"additional","affiliation":[{"name":"Department of Biostatistics, City University of Hong Kong , Kowloon Tong, Hong Kong"}],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"Kin-Yat","family":"Liu","sequence":"additional","affiliation":[{"name":"Department of Statistics, The Chinese University of Hong Kong , Shatin, New Territories, Hong Kong"}],"role":[{"role":"author","vocabulary":"crossref"}]},{"ORCID":"https:\/\/orcid.org\/0000-0003-3276-1392","authenticated-orcid":false,"given":"Guosheng","family":"Yin","sequence":"additional","affiliation":[{"name":"School of Computing and Data Science, The University of Hong Kong , Pokfulam Road, Hong Kong"}],"role":[{"role":"author","vocabulary":"crossref"}]},{"ORCID":"https:\/\/orcid.org\/0000-0002-4938-7352","authenticated-orcid":false,"given":"Xingqiu","family":"Zhao","sequence":"additional","affiliation":[{"name":"Department of Applied Mathematics, The Hong Kong Polytechnic University , Hung Hom, Kowloon, Hong Kong"}],"role":[{"role":"author","vocabulary":"crossref"}]}],"member":"286","published-online":{"date-parts":[[2025,3,7]]},"reference":[{"key":"2025062506174709000_asaf011-B1","doi-asserted-by":"crossref","first-page":"429","DOI":"10.1093\/biomet\/66.3.429","article-title":"Linear regression with censored data","volume":"66","author":"Buckley","year":"1979","journal-title":"Biometrika"},{"key":"2025062506174709000_asaf011-B2","doi-asserted-by":"crossref","first-page":"1201","DOI":"10.1080\/01621459.2012.716337","article-title":"Minimax and adaptive prediction for functional linear regression","volume":"107","author":"Cai","year":"2012","journal-title":"J. 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