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Nonparametric regression with doubly truncated data

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  • Moreira, C.
  • de Uña-Álvarez, J.
  • Meira-Machado, L.

Abstract

Nonparametric regression with a doubly truncated response is introduced. Local constant and local linear kernel-type estimators are proposed. Asymptotic expressions for the bias and the variance of the estimators are obtained, showing the deterioration provoked by the random truncation. To solve the crucial problem of bandwidth choice, two different bandwidth selectors based on plug-in and cross-validation ideas are introduced. The performance of both the estimators and the bandwidth selectors is investigated through simulations. A real data illustration is included. The main conclusion is that the introduced regression methods perform satisfactorily in the complicated scenario of random double truncation.

Suggested Citation

  • Moreira, C. & de Uña-Álvarez, J. & Meira-Machado, L., 2016. "Nonparametric regression with doubly truncated data," Computational Statistics & Data Analysis, Elsevier, vol. 93(C), pages 294-307.
    • Handle: RePEc:eee:csdana:v:93:y:2016:i:c:p:294-307
    DOI: 10.1016/j.csda.2014.03.017
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    References listed on IDEAS

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    1. Elias Ould-Saïd & Mohamed Lemdani, 2006. "Asymptotic Properties of a Nonparametric Regression Function Estimator with Randomly Truncated Data," Annals of the Institute of Statistical Mathematics, Springer;The Institute of Statistical Mathematics, vol. 58(2), pages 357-378, June.
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    3. Pao-sheng Shen, 2010. "Nonparametric analysis of doubly truncated data," Annals of the Institute of Statistical Mathematics, Springer;The Institute of Statistical Mathematics, vol. 62(5), pages 835-853, October.
    4. Han-Ying Liang & Jacobo Uña-Álvarez & María Iglesias-Pérez, 2011. "Local polynomial estimation of a conditional mean function with dependent truncated data," TEST: An Official Journal of the Spanish Society of Statistics and Operations Research, Springer;Sociedad de Estadística e Investigación Operativa, vol. 20(3), pages 653-677, November.
    5. Martin, Emily C. & Betensky, Rebecca A., 2005. "Testing Quasi-Independence of Failure and Truncation Times via Conditional Kendall's Tau," Journal of the American Statistical Association, American Statistical Association, vol. 100, pages 484-492, June.
    6. Liang, Han-Ying & de Uña-Álvarez, Jacobo, 2011. "Wavelet estimation of conditional density with truncated, censored and dependent data," Journal of Multivariate Analysis, Elsevier, vol. 102(3), pages 448-467, March.
    7. Moreira, Carla & de Uña-Álvarez, Jacobo & Crujeiras, Rosa M., 2010. "DTDA: An R Package to Analyze Randomly Truncated Data," Journal of Statistical Software, Foundation for Open Access Statistics, vol. 37(i07).
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    Cited by:

    1. Shen, Pao-sheng & Hsu, Huichen, 2020. "Conditional maximum likelihood estimation for semiparametric transformation models with doubly truncated data," Computational Statistics & Data Analysis, Elsevier, vol. 144(C).
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    4. Lior Rennert & Sharon X. Xie, 2018. "Cox regression model with doubly truncated data," Biometrics, The International Biometric Society, vol. 74(2), pages 725-733, June.

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