IDEAS home Printed from https://ideas.repec.org/a/taf/jnlasa/v108y2013i503p971-982.html
   My bibliography  Save this article

Nonparametric Estimation of Conditional Distributions and Rank-Tracking Probabilities With Time-Varying Transformation Models in Longitudinal Studies

Author

Listed:
  • Colin O. Wu
  • Xin Tian

Abstract

An objective of longitudinal analysis is to estimate the conditional distributions of an outcome variable through a regression model. The approaches based on modeling the conditional means are not appropriate for this task when the conditional distributions are skewed or cannot be approximated by a normal distribution through a known transformation. We study a class of time-varying transformation models and a two-step smoothing method for the estimation of the conditional distribution functions. Based on our models, we propose a rank-tracking probability and a rank-tracking probability ratio to measure the strength of tracking ability of an outcome variable at two different time points. Our models and estimation method can be applied to a wide range of scientific objectives that cannot be evaluated by the conditional mean-based models. We derive the asymptotic properties for the two-step local polynomial estimators of the conditional distribution functions. Finite sample properties of our procedures are investigated through a simulation study. Application of our models and estimation method is demonstrated through an epidemiological study of childhood growth and blood pressure. Supplementary materials for this article are available online.

Suggested Citation

  • Colin O. Wu & Xin Tian, 2013. "Nonparametric Estimation of Conditional Distributions and Rank-Tracking Probabilities With Time-Varying Transformation Models in Longitudinal Studies," Journal of the American Statistical Association, Taylor & Francis Journals, vol. 108(503), pages 971-982, September.
  • Handle: RePEc:taf:jnlasa:v:108:y:2013:i:503:p:971-982
    DOI: 10.1080/01621459.2013.808949
    as

    Download full text from publisher

    File URL: http://hdl.handle.net/10.1080/01621459.2013.808949
    Download Restriction: Access to full text is restricted to subscribers.

    File URL: https://libkey.io/10.1080/01621459.2013.808949?utm_source=ideas
    LibKey link: if access is restricted and if your library uses this service, LibKey will redirect you to where you can use your library subscription to access this item
    ---><---

    As the access to this document is restricted, you may want to search for a different version of it.

    References listed on IDEAS

    as
    1. Colin Wu & Xin Tian & Jarvis Yu, 2010. "Nonparametric estimation for time-varying transformation models with longitudinal data," Journal of Nonparametric Statistics, Taylor & Francis Journals, vol. 22(2), pages 133-147.
    2. Hall, Peter & Wolff, Rodney C. L. & Yao, Qiwei, 1999. "Methods for estimating a conditional distribution function," LSE Research Online Documents on Economics 6631, London School of Economics and Political Science, LSE Library.
    Full references (including those not matched with items on IDEAS)

    Citations

    Citations are extracted by the CitEc Project, subscribe to its RSS feed for this item.
    as


    Cited by:

    1. Ming Xiong & Ao Yuan & Hong-Bin Fang & Colin O. Wu & Ming T. Tan, 2022. "Estimation and Hypothesis Test for Mean Curve with Functional Data by Reproducing Kernel Hilbert Space Methods, with Applications in Biostatistics," Mathematics, MDPI, vol. 10(23), pages 1-17, December.
    2. Minjung Kwak, 2017. "Estimation and inference of the joint conditional distribution for multivariate longitudinal data using nonparametric copulas," Journal of Nonparametric Statistics, Taylor & Francis Journals, vol. 29(3), pages 491-514, July.
    3. Chen, Yaqing & Dawson, Matthew & Müller, Hans-Georg, 2020. "Rank dynamics for functional data," Computational Statistics & Data Analysis, Elsevier, vol. 149(C).

    Most related items

    These are the items that most often cite the same works as this one and are cited by the same works as this one.
    1. Mohammed Chowdhury & Colin Wu & Reza Modarres, 2018. "Nonparametric estimation of conditional distribution functions with longitudinal data and time-varying parametric models," Metrika: International Journal for Theoretical and Applied Statistics, Springer, vol. 81(1), pages 61-83, January.
    2. Sokbae Lee & Oliver Linton & Yoon-Jae Whang, 2009. "Testing for Stochastic Monotonicity," Econometrica, Econometric Society, vol. 77(2), pages 585-602, March.
    3. Fan, Yanqin & Liu, Ruixuan, 2016. "A direct approach to inference in nonparametric and semiparametric quantile models," Journal of Econometrics, Elsevier, vol. 191(1), pages 196-216.
    4. Victor Chernozhukov & Iván Fernández‐Val & Blaise Melly, 2013. "Inference on Counterfactual Distributions," Econometrica, Econometric Society, vol. 81(6), pages 2205-2268, November.
    5. Martins-Filho, Carlos & Ziegelmann, Flávio Augusto & Torrent, Hudson da Silva, 2013. "Local Exponential Frontier Estimation," Brazilian Review of Econometrics, Sociedade Brasileira de Econometria - SBE, vol. 33(2), November.
    6. Dingshi Tian & Zongwu Cai & Ying Fang, 2018. "Econometric Modeling of Risk Measures: A Selective Review of the Recent Literature," WORKING PAPERS SERIES IN THEORETICAL AND APPLIED ECONOMICS 201807, University of Kansas, Department of Economics, revised Oct 2018.
    7. Frandsen, Brigham R. & Frölich, Markus & Melly, Blaise, 2012. "Quantile treatment effects in the regression discontinuity design," Journal of Econometrics, Elsevier, vol. 168(2), pages 382-395.
    8. Xiong, Xianzhu & Ou, Meijuan & Chen, Ailian, 2021. "Reweighted Nadaraya–Watson estimation of conditional density function in the right-censored model," Statistics & Probability Letters, Elsevier, vol. 168(C).
    9. Bhattacharya, Debopam & Dupas, Pascaline, 2012. "Inferring welfare maximizing treatment assignment under budget constraints," Journal of Econometrics, Elsevier, vol. 167(1), pages 168-196.
    10. Dette, Holger & Volgushev, Stanislav, 2007. "Non-crossing nonparametric estimates of quantile curves," Technical Reports 2007,18, Technische Universität Dortmund, Sonderforschungsbereich 475: Komplexitätsreduktion in multivariaten Datenstrukturen.
    11. Ekaterina Selezneva & Philippe Van Kerm, 2016. "A distribution-sensitive examination of the gender wage gap in Germany," The Journal of Economic Inequality, Springer;Society for the Study of Economic Inequality, vol. 14(1), pages 21-40, March.
    12. Isabel Casas & Irene Gijbels, 2009. "Unstable volatility functions: the break preserving local linear estimator," CREATES Research Papers 2009-48, Department of Economics and Business Economics, Aarhus University.
    13. Yiguo Sun & Thanasis Stengos, 2008. "The absolute health income hypothesis revisited: a semiparametric quantile regression approach," Empirical Economics, Springer, vol. 35(2), pages 395-412, September.
    14. Lorenzo Tedesco & Jad Beyhum & Ingrid Van Keilegom, 2023. "Instrumental variable estimation of the proportional hazards model by presmoothing," Papers 2309.02183, arXiv.org.
    15. François Gerard & Miikka Rokkanen & Christoph Rothe, 2020. "Bounds on treatment effects in regression discontinuity designs with a manipulated running variable," Quantitative Economics, Econometric Society, vol. 11(3), pages 839-870, July.
    16. Valentina Corradi & Norman Swanson & Walter Distaso, 2006. "Predictive Inference for Integrated Volatility," Departmental Working Papers 200616, Rutgers University, Department of Economics.
    17. Abdelaati Daouia & Byeong U. Park, 2013. "On Projection-type Estimators of Multivariate Isotonic Functions," Scandinavian Journal of Statistics, Danish Society for Theoretical Statistics;Finnish Statistical Society;Norwegian Statistical Association;Swedish Statistical Association, vol. 40(2), pages 363-386, June.
    18. Alexander Henzi & Johanna F. Ziegel & Tilmann Gneiting, 2021. "Isotonic distributional regression," Journal of the Royal Statistical Society Series B, Royal Statistical Society, vol. 83(5), pages 963-993, November.
    19. Chiang, Chin-Tsang & Huang, Ming-Yueh, 2012. "New estimation and inference procedures for a single-index conditional distribution model," Journal of Multivariate Analysis, Elsevier, vol. 111(C), pages 271-285.
    20. Gerard, François & Rothe, Christoph & Rokkanen, Miikka, 2016. "Bounds on Treatment Effects in Regression Discontinuity Designs under Manipulation of the Running Variable, with an Application," CEPR Discussion Papers 11668, C.E.P.R. Discussion Papers.

    More about this item

    Statistics

    Access and download statistics

    Corrections

    All material on this site has been provided by the respective publishers and authors. You can help correct errors and omissions. When requesting a correction, please mention this item's handle: RePEc:taf:jnlasa:v:108:y:2013:i:503:p:971-982. See general information about how to correct material in RePEc.

    If you have authored this item and are not yet registered with RePEc, we encourage you to do it here. This allows to link your profile to this item. It also allows you to accept potential citations to this item that we are uncertain about.

    If CitEc recognized a bibliographic reference but did not link an item in RePEc to it, you can help with this form .

    If you know of missing items citing this one, you can help us creating those links by adding the relevant references in the same way as above, for each refering item. If you are a registered author of this item, you may also want to check the "citations" tab in your RePEc Author Service profile, as there may be some citations waiting for confirmation.

    For technical questions regarding this item, or to correct its authors, title, abstract, bibliographic or download information, contact: Chris Longhurst (email available below). General contact details of provider: http://www.tandfonline.com/UASA20 .

    Please note that corrections may take a couple of weeks to filter through the various RePEc services.

    IDEAS is a RePEc service. RePEc uses bibliographic data supplied by the respective publishers.