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Original Articles

Product limit estimates: a generalized maximum likelihood study

Pages 3117-3132 | Received 01 Feb 1987, Published online: 27 Jun 2007

Keep up to date with the latest research on this topic with citation updates for this article.

Read on this site (19)

Pao-sheng Shen. (2020) Empirical likelihood ratio confidence intervals in terms of cumulative hazard function for left-truncated and right-censored data. Communications in Statistics - Theory and Methods 49:18, pages 4571-4586.
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Pao-sheng Shen & Li Ning Weng. (2018) The Cox–Aalen model for left-truncated and right-censored data. Communications in Statistics - Theory and Methods 47:21, pages 5357-5368.
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Wei Chen, Dehui Wang & Yanfeng Li. (2015) A class of tests of proportional hazards assumption for left-truncated and right-censored data. Journal of Applied Statistics 42:11, pages 2307-2320.
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Pao-Sheng Shen. (2014) Analysing truncated data with semiparametric transformation models. Journal of Statistical Computation and Simulation 84:11, pages 2474-2485.
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Pao-Sheng Shen. (2014) A weighted quantile regression for left-truncated and right-censored data. Journal of Statistical Computation and Simulation 84:3, pages 596-604.
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Pao-Sheng Shen. (2013) Nonparametric Estimation of the Bivariate Distribution Function with Doubly Truncated Data. Communications in Statistics - Theory and Methods 42:21, pages 3805-3818.
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Jane Paik Kim, Wenbin Lu, Tony Sit & Zhiliang Ying. (2013) A Unified Approach to Semiparametric Transformation Models Under General Biased Sampling Schemes. Journal of the American Statistical Association 108:501, pages 217-227.
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Pao-Sheng Shen. (2012) Nonparametric Estimators of the Distribution Function for One Modified Model of Current Status Data. Communications in Statistics - Theory and Methods 41:22, pages 4096-4106.
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Pao-sheng Shen. (2012) Nonparametric Estimation of the Bivariate Distribution Function with Doubly Censored Data. Communications in Statistics - Theory and Methods 41:2, pages 195-211.
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Pao-Sheng Shen. (2007) A General Class of Test Procedures for Left-Truncated and Right-Censored Data. Communications in Statistics - Theory and Methods 36:16, pages 2913-2925.
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Pao-Sheng Shen. (2007) A general semiparametric model for left-truncated and right-censored data. Journal of Nonparametric Statistics 19:3, pages 113-129.
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Pao-Sheng Shen. (2005) Estimation of the truncation probability with left-truncated and right-censored data. Journal of Nonparametric Statistics 17:8, pages 957-969.
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MichaelG. Akritas & MichaelP. LaValley. (2005) A generalized product-limit estimator for truncated data. Journal of Nonparametric Statistics 17:6, pages 643-663.
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Pao-Sheng Shen. (2005) Nonparametric Bivariate Estimation with Left-Truncated and Right-Censored Data. Communications in Statistics - Theory and Methods 34:7, pages 1675-1685.
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Pao-sheng Shen. (2003) The Product-Limit Estimate as an Inverse-Probability-Weighted Average. Communications in Statistics - Theory and Methods 32:6, pages 1119-1133.
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Mei-Cheng Wang. (1992) The Analysis of Retrospectively Ascertained Data in the Presence of Reporting Delays. Journal of the American Statistical Association 87:418, pages 397-406.
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Mei-Cheng Wang. (1991) Nonparametric Estimation from Cross-Sectional Survival Data. Journal of the American Statistical Association 86:413, pages 130-143.
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Articles from other publishers (27)

Rebecca A. Betensky, Jing Qian & Jingyao Hou. (2022) Nonparametric and semiparametric estimation with sequentially truncated survival data. Biometrics 79:2, pages 1000-1013.
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Jackson P. Lautier, Vladimir Pozdnyakov & Jun Yan. (2023) Estimating a discrete distribution subject to random left-truncation with an application to structured finance. Econometrics and Statistics.
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Luis A. Souto Arias, Pasquale Cirillo & Cornelis W. Oosterlee. (2023) Estimation of reinforced urn processes under left-truncation and right-censoring. Royal Society Open Science 10:3.
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Pao-sheng Shen, Yingwei Peng, Hsin-Jen Chen & Chyong-Mei Chen. (2021) Maximum likelihood estimation for length-biased and interval-censored data with a nonsusceptible fraction. Lifetime Data Analysis 28:1, pages 68-88.
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Maria Pedrosa-Laza, Ana López-Cheda & Ricardo Cao. (2021) Cure models to estimate time until hospitalization due to COVID-19. Applied Intelligence 52:1, pages 794-807.
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Yidan Shi, Leilei Zeng, Mary E. Thompson & Suzanne L. Tyas. (2021) Augmented likelihood for incorporating auxiliary information into left-truncated data. Lifetime Data Analysis 27:3, pages 460-480.
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Pao-sheng Shen & Huichen Hsu. (2020) Conditional maximum likelihood estimation for semiparametric transformation models with doubly truncated data. Computational Statistics & Data Analysis 144, pages 106862.
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Aniket Roy, Rahul Dixit, Ruchira Naskar & Rajat Subhra ChakrabortyAchim Dörre & Takeshi Emura. 2020. Digital Image Forensics. Digital Image Forensics 63 74 .
Chyong-Mei Chen & Pao-Sheng Shen. (2017) Conditional maximum likelihood estimation in semiparametric transformation model with LTRC data. Lifetime Data Analysis 24:2, pages 250-272.
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Pao-sheng Shen. (2015) A self-consistent estimator of survival function with interval-censored and left-truncated data. Journal of the Korean Statistical Society 44:2, pages 211-220.
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Han-Ying Liang, Jacobo de Uña-Álvarez & María del Carmen Iglesias-Pérez. (2012) Asymptotic properties of conditional distribution estimator with truncated, censored and dependent data. TEST 21:4, pages 790-810.
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Pao-sheng Shen. (2011) Analysis of left-truncated right-censored or doubly censored data with linear transformation models. TEST 21:3, pages 584-603.
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Yu-Ru Su & Jane-Ling Wang. (2012) Modeling left-truncated and right-censored survival data with longitudinal covariates. The Annals of Statistics 40:3.
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Pao-sheng Shen. (2010) Nonparametric estimators of the survival function with twice censored data. Annals of the Institute of Statistical Mathematics 63:6, pages 1207-1219.
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Han-Ying Liang & Jacobo de Uña-Álvarez. (2011) Wavelet estimation of conditional density with truncated, censored and dependent data. Journal of Multivariate Analysis 102:3, pages 448-467.
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Pao-sheng Shen. (2010) Nonparametric estimation with doubly censored and truncated data. Computational Statistics 26:1, pages 145-157.
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Pao-sheng Shen. (2008) Nonparametric analysis of doubly truncated data. Annals of the Institute of Statistical Mathematics 62:5, pages 835-853.
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Pao-sheng Shen. (2010) A class of semiparametric rank-based tests for right-truncated data. Statistics & Probability Letters 80:17-18, pages 1459-1466.
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Pao-sheng Shen. (2010) An inverse-probability-weighted approach to the estimation of distribution function with middle-censored data. Journal of Statistical Planning and Inference 140:7, pages 1844-1851.
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Pao-sheng Shen. (2009) Semiparametric analysis of survival data with left truncation and right censoring. Computational Statistics & Data Analysis 53:12, pages 4417-4432.
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Pao-sheng Shen. (2007) A class of rank-based test for left-truncated and right-censored data. Annals of the Institute of Statistical Mathematics 61:2, pages 461-476.
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Pao-sheng Shen. (2009) An inverse-probability-weighted approach to the estimation of distribution function with doubly censored data. Statistics & Probability Letters 79:9, pages 1269-1276.
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Pao-sheng Shen. (2006) An inverse-probability-weighted approach to estimation of the bivariate survival function under left-truncation and right-censoring. Journal of Statistical Planning and Inference 136:12, pages 4365-4384.
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Yong Zhou & Liu-quan Sun. (2005) Sequential Confidence Bands for Quantile Densities Under Truncated and Censored Data. Acta Mathematicae Applicatae Sinica, English Series 21:2, pages 311-322.
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Guoxing Soon & Michael Woodroofe. (1996) Nonparametric estimation and consistency for renewal processes. Journal of Statistical Planning and Inference 53:2, pages 171-195.
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Minggao Gu. (1995) Convergence of increments for cumulative hazard function in a mixed censorship-truncation model with application to hazard estimators. Statistics & Probability Letters 23:2, pages 135-139.
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Luis Souto Arias & Pasquale Cirillo. (2020) Estimation for Uni-variate and Bi-variate Reinforced Urn Processes Under Left-Truncation and Right-Censoring. SSRN Electronic Journal.
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