{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2025,10,11]],"date-time":"2025-10-11T02:29:26Z","timestamp":1760149766023,"version":"build-2065373602"},"reference-count":27,"publisher":"MDPI AG","issue":"9","license":[{"start":{"date-parts":[[2023,9,7]],"date-time":"2023-09-07T00:00:00Z","timestamp":1694044800000},"content-version":"vor","delay-in-days":0,"URL":"https:\/\/creativecommons.org\/licenses\/by\/4.0\/"}],"funder":[{"name":"TUBITAK 1002 project","award":["122F045"],"award-info":[{"award-number":["122F045"]}]}],"content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":["Entropy"],"abstract":"<jats:p>This paper introduces a modified local linear estimator (LLR) for partially linear additive models (PLAM) when the response variable is subject to random right-censoring. In the case of modeling right-censored data, PLAM offers a more flexible and realistic approach to the estimation procedure by involving multiple parametric and nonparametric components. This differs from the widely used partially linear models that feature a univariate nonparametric function. The LLR method is employed to estimate unknown smooth functions using a modified backfitting algorithm, delivering a non-iterative solution for the right-censored PLAM. To address the censorship issue, three approaches are employed: synthetic data transformation (ST), Kaplan\u2013Meier weights (KMW), and the kNN imputation technique (kNNI). Asymptotic properties of the modified backfitting estimators are detailed for both ST and KMW solutions. The advantages and disadvantages of these methods are discussed both theoretically and practically. Comprehensive simulation studies and real-world data examples are conducted to assess the performance of the introduced estimators. The results indicate that LLR performs well with both KMW and kNNI in the majority of scenarios, along with a real data example.<\/jats:p>","DOI":"10.3390\/e25091307","type":"journal-article","created":{"date-parts":[[2023,9,7]],"date-time":"2023-09-07T10:09:50Z","timestamp":1694081390000},"page":"1307","update-policy":"https:\/\/doi.org\/10.3390\/mdpi_crossmark_policy","source":"Crossref","is-referenced-by-count":1,"title":["Modified Local Linear Estimators in Partially Linear Additive Models with Right-Censored Data Based on Different Censorship Solution Techniques"],"prefix":"10.3390","volume":"25","author":[{"ORCID":"https:\/\/orcid.org\/0000-0002-9871-4700","authenticated-orcid":false,"given":"Ersin","family":"Y\u0131lmaz","sequence":"first","affiliation":[{"name":"Department of Statistics, Mugla S\u0131tk\u0131 Kocman University, Mugla 48000, Turkey"}],"role":[{"role":"author","vocabulary":"crossref"}]},{"ORCID":"https:\/\/orcid.org\/0000-0001-8393-1270","authenticated-orcid":false,"given":"Dursun","family":"Ayd\u0131n","sequence":"additional","affiliation":[{"name":"Department of Statistics, Mugla S\u0131tk\u0131 Kocman University, Mugla 48000, Turkey"}],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"S. Ejaz","family":"Ahmed","sequence":"additional","affiliation":[{"name":"Department of Mathematics and Statistics, Brock University, St. Catharines, ON L2S 3A1, Canada"}],"role":[{"role":"author","vocabulary":"crossref"}]}],"member":"1968","published-online":{"date-parts":[[2023,9,7]]},"reference":[{"key":"ref_1","doi-asserted-by":"crossref","unstructured":"Ruppert, D., Wand, M.P., and Carroll, R.J. (2003). Semiparametric Regression (No. 12), Cambridge University Press.","DOI":"10.1017\/CBO9780511755453"},{"key":"ref_2","doi-asserted-by":"crossref","first-page":"1099","DOI":"10.1198\/jasa.2011.tm10281","article-title":"Linear or nonlinear? Automatic structure discovery for partially linear models","volume":"106","author":"Zhang","year":"2011","journal-title":"J. Am. Stat. Assoc."},{"key":"ref_3","doi-asserted-by":"crossref","first-page":"1","DOI":"10.1006\/jmva.1996.1642","article-title":"Local linear estimation in partly linear models","volume":"60","author":"Hamilton","year":"1997","journal-title":"J. Multivar. Anal."},{"key":"ref_4","doi-asserted-by":"crossref","first-page":"1470","DOI":"10.1080\/00949655.2018.1439032","article-title":"Modified estimators in semiparametric regression models with right-censored data","volume":"88","author":"Aydin","year":"2018","journal-title":"J. Stat. Comput. Simul."},{"key":"ref_5","first-page":"95","article-title":"Penalized spline smoothing using Kaplan-Meier weights in semiparametric censored regression models","volume":"46","author":"Orbe","year":"2022","journal-title":"Stat. Oper. Res. Trans."},{"key":"ref_6","doi-asserted-by":"crossref","first-page":"372","DOI":"10.1177\/09622802211061635","article-title":"Comparison of parametric and semi-parametric models with randomly right-censored data by weighted estimators: Two applications in colon cancer and hepatocellular carcinoma datasets","volume":"31","author":"Yenilmez","year":"2022","journal-title":"Stat. Methods Med. Res."},{"key":"ref_7","doi-asserted-by":"crossref","first-page":"704","DOI":"10.1111\/j.0006-341X.1999.00704.x","article-title":"Kriging with nonparametric variance function estimation","volume":"55","author":"Opsomer","year":"1999","journal-title":"Biometrics"},{"key":"ref_8","doi-asserted-by":"crossref","first-page":"252","DOI":"10.1016\/j.jeconom.2010.05.005","article-title":"Characterization of the asymptotic distribution of semiparametric M-estimators","volume":"159","author":"Ichimura","year":"2010","journal-title":"J. Econom."},{"key":"ref_9","doi-asserted-by":"crossref","first-page":"e1605","DOI":"10.1002\/wics.1605","article-title":"A survey of smoothing techniques based on a backfitting algorithm in estimation of semiparametric additive models","volume":"15","author":"Ahmed","year":"2023","journal-title":"Wiley Interdiscip. Rev. Comput. Stat."},{"key":"ref_10","first-page":"1089","article-title":"Nonlinear censored regression","volume":"9","author":"Stute","year":"1999","journal-title":"Stat. Sin."},{"key":"ref_11","doi-asserted-by":"crossref","first-page":"985","DOI":"10.1080\/00949655.2019.1572757","article-title":"Estimation of semiparametric regression model with right-censored high-dimensional data","volume":"89","author":"Ahmed","year":"2019","journal-title":"J. Stat. Comput. Simul."},{"key":"ref_12","doi-asserted-by":"crossref","first-page":"1276","DOI":"10.1214\/aos\/1176345644","article-title":"Regression analysis with randomly right-censored data","volume":"9","author":"Koul","year":"1981","journal-title":"Ann. Stat."},{"key":"ref_13","doi-asserted-by":"crossref","first-page":"89","DOI":"10.1006\/jmva.1993.1028","article-title":"Consistent estimation under random censorship when covariables are present","volume":"45","author":"Stute","year":"1993","journal-title":"J. Multivar. Anal."},{"key":"ref_14","doi-asserted-by":"crossref","first-page":"2541","DOI":"10.1016\/j.jss.2012.05.073","article-title":"Nearest neighbor selection for iteratively kNN imputation","volume":"85","author":"Zhang","year":"2012","journal-title":"J. Syst. Softw."},{"key":"ref_15","unstructured":"Ahmed, S.E., Aydin, D., and Y\u0131lmaz, E. (2019). International Conference on Management Science and Engineering Management, Springer International Publishing."},{"key":"ref_16","unstructured":"Cartwright, M.H., Shepperd, M.J., and Song, Q. (2004, January 5). Dealing with missing software project data. Proceedings of the 5th International Workshop on Enterprise Networking and Computing in Healthcare Industry (IEEE Cat. No. 03EX717), Sydney, Australia."},{"key":"ref_17","unstructured":"Hastie, T.J., and Tibshirani, R.J. (1990). Generalized Additive Models, CRC Press."},{"key":"ref_18","doi-asserted-by":"crossref","unstructured":"H\u00e4rdle, W., M\u00fcller, M., Sperlich, S., and Werwatz, A. (2004). Nonparametric and Semiparametric Models, Springer.","DOI":"10.1007\/978-3-642-17146-8"},{"key":"ref_19","first-page":"453","article-title":"Linear smoothers and additive models","volume":"17","author":"Buja","year":"1989","journal-title":"Ann. Stat."},{"key":"ref_20","first-page":"715","article-title":"A root-n consistent backfitting estimator for semiparametric additive modeling","volume":"8","author":"Opsomer","year":"1999","journal-title":"J. Comput. Graph. Stat."},{"key":"ref_21","doi-asserted-by":"crossref","first-page":"809","DOI":"10.1080\/10485252.2012.716155","article-title":"Statistical inference on semi-parametric partial linear additive models","volume":"24","author":"Wei","year":"2012","journal-title":"J. Nonparametr. Stat."},{"key":"ref_22","doi-asserted-by":"crossref","first-page":"66","DOI":"10.1198\/1061860043056","article-title":"Generalized cross-validation for bandwidth selection of backfitting estimates in generalized additive models","volume":"13","author":"Kauermann","year":"2004","journal-title":"J. Comput. Graph. Stat."},{"key":"ref_23","doi-asserted-by":"crossref","first-page":"265","DOI":"10.1016\/0378-3758(94)00096-E","article-title":"Bandwidth selection in nonparametric regression with general errors","volume":"44","author":"Chu","year":"1995","journal-title":"J. Stat. Plan. Inference"},{"key":"ref_24","doi-asserted-by":"crossref","first-page":"129","DOI":"10.2307\/2530813","article-title":"Nonparametric estimation of a multivariate distribution in the presence of censoring","volume":"39","author":"Hanley","year":"1983","journal-title":"Biometrics"},{"key":"ref_25","doi-asserted-by":"crossref","first-page":"256","DOI":"10.1007\/s10985-010-9175-8","article-title":"Linear regression analysis of survival data with missing censoring indicators","volume":"17","author":"Wang","year":"2011","journal-title":"Lifetime Data Anal."},{"key":"ref_26","first-page":"1","article-title":"Semiparametric regression estimates based on some transformation techniques for right-censored data","volume":"20","author":"Aydin","year":"2019","journal-title":"Eski\u015fehir Tech. Univ. J. Sci. Technol. A\u2014Appl. Sci. Eng."},{"key":"ref_27","doi-asserted-by":"crossref","unstructured":"Li, L., Yan, J., Xu, J., Liu, C.-Q., Zhen, Z.-J., Chen, H.-W., Ji, Y., Wu, Z.-P., Hu, J.-Y., and Zheng, L. (2014). CXCL17 expression predicts poor prognosis and correlates with adverse immune infiltration in hepatocellular carcinoma. 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