IDEAS home Printed from https://ideas.repec.org/a/spr/stpapr/v59y2018i1d10.1007_s00362-016-0756-9.html
   My bibliography  Save this article

The selection of the number of terms in an orthogonal series cumulative function estimator

Author

Listed:
  • Nora Saadi

    (University of Bejaia)

  • Smail Adjabi

    (University of Bejaia)

  • Ali Gannoun

    (University of Montpellier 2)

Abstract

Let h(.) be a continuous, strictly positive probability density function over an interval [a, b] and H(.) its associated cumulative distribution function (cdf). Given a sample set $$X_{1},\ldots ,X_{n}$$ X 1 , … , X n of independent identically distributed variables, we want to estimate H(.) from this sample set. The present work has two goals. The first one is to propose an estimator of a cdf based on an orthogonal trigonometric series and to give its statistical and asymptotic proprieties (bias, variance, mean square error, mean integrated squared error, convergence of the bias, convergence of variance, convergence of the mean squared error, convergence of the mean integrated squared error, uniform convergence in probability and the rate of convergence of the mean integrated squared error). The second is to introduce a new method for the selection of a “smoothing parameter”. The comparison by simulation between this method and Kronmal–Tarter’s method, shows that the new method is more performant in the sense of the mean integrated square error.

Suggested Citation

  • Nora Saadi & Smail Adjabi & Ali Gannoun, 2018. "The selection of the number of terms in an orthogonal series cumulative function estimator," Statistical Papers, Springer, vol. 59(1), pages 127-152, March.
    • Handle: RePEc:spr:stpapr:v:59:y:2018:i:1:d:10.1007_s00362-016-0756-9
    DOI: 10.1007/s00362-016-0756-9
    as

    Download full text from publisher

    File URL: http://link.springer.com/10.1007/s00362-016-0756-9
    File Function: Abstract
    Download Restriction: Access to the full text of the articles in this series is restricted.
    File URL: https://libkey.io/10.1007/s00362-016-0756-9?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. Martin B. Hansen & Steffen L. Lauritzen, 2002. "Nonparametric Bayes inference for concave distribution functions," Statistica Neerlandica, Netherlands Society for Statistics and Operations Research, vol. 56(1), pages 110-127, February.
    2. Stephen T. Buckland, 1992. "Fitting Density Functions with Polynomials," Journal of the Royal Statistical Society Series C, Royal Statistical Society, vol. 41(1), pages 63-76, March.
    3. F. Perron & K. Mengersen, 2001. "Bayesian Nonparametric Modeling Using Mixtures of Triangular Distributions," Biometrics, The International Biometric Society, vol. 57(2), pages 518-528, June.
    4. Jones, M. C., 1990. "The performance of kernel density functions in kernel distribution function estimation," Statistics & Probability Letters, Elsevier, vol. 9(2), pages 129-132, February.
    Full references (including those not matched with items on IDEAS)

    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. Jungmin An & Dong-Kwan Kim & Jinyeong Lee & Sung-Kwan Joo, 2021. "Least Squares Monte Carlo Simulation-Based Decision-Making Method for Photovoltaic Investment in Korea," Sustainability, MDPI, vol. 13(19), pages 1-14, September.
    2. Hussein Khraibani & Bilal Nehme & Olivier Strauss, 2018. "Interval Estimation of Value-at-Risk Based on Nonparametric Models," Econometrics, MDPI, vol. 6(4), pages 1-30, December.
    3. Minglu Ma & Qiang Wang, 2022. "Assessment and Forecast of Green Total Factor Energy Efficiency in the Yellow River Basin—A Perspective Distinguishing the Upper, Middle and Lower Stream," Sustainability, MDPI, vol. 14(5), pages 1-23, February.
    4. Shingo Shirahata & In-Sun Chu, 1992. "Integrated squared error of kernel-type estimator of distribution function," Annals of the Institute of Statistical Mathematics, Springer;The Institute of Statistical Mathematics, vol. 44(3), pages 579-591, September.
    5. Ho, Chi-san & Damien, Paul & Walker, Stephen, 2017. "Bayesian mode regression using mixtures of triangular densities," Journal of Econometrics, Elsevier, vol. 197(2), pages 273-283.
    6. McVinish, R. & Mengersen, K., 2008. "Semiparametric Bayesian circular statistics," Computational Statistics & Data Analysis, Elsevier, vol. 52(10), pages 4722-4730, June.
    7. Funke, Benedikt & Palmes, Christian, 2017. "A note on estimating cumulative distribution functions by the use of convolution power kernels," Statistics & Probability Letters, Elsevier, vol. 121(C), pages 90-98.
    8. repec:jss:jstsof:40:i05 is not listed on IDEAS
    9. Athanasios Kottas & Milovan Krnjajić, 2009. "Bayesian Semiparametric Modelling in Quantile Regression," Scandinavian Journal of Statistics, Danish Society for Theoretical Statistics;Finnish Statistical Society;Norwegian Statistical Association;Swedish Statistical Association, vol. 36(2), pages 297-319, June.
    10. Patricio Maturana-Russel & Renate Meyer, 2021. "Bayesian spectral density estimation using P-splines with quantile-based knot placement," Computational Statistics, Springer, vol. 36(3), pages 2055-2077, September.
    11. Wenbin Lu & Lexin Li, 2011. "Sufficient Dimension Reduction for Censored Regressions," Biometrics, The International Biometric Society, vol. 67(2), pages 513-523, June.
    12. Bouzebda, Salim & Slaoui, Yousri, 2022. "Nonparametric recursive method for moment generating function kernel-type estimators," Statistics & Probability Letters, Elsevier, vol. 184(C).
    13. Weining Shen & Jing Ning & Ying Yuan & Anna S. Lok & Ziding Feng, 2018. "Model†free scoring system for risk prediction with application to hepatocellular carcinoma study," Biometrics, The International Biometric Society, vol. 74(1), pages 239-248, March.
    14. David L. Borchers & Tiago A. Marques, 2017. "From distance sampling to spatial capture–recapture," AStA Advances in Statistical Analysis, Springer;German Statistical Society, vol. 101(4), pages 475-494, October.
    15. D. Blanke & D. Bosq, 2018. "Polygonal smoothing of the empirical distribution function," Statistical Inference for Stochastic Processes, Springer, vol. 21(2), pages 263-287, July.
    16. Cai, Bo & Meyer, Renate, 2011. "Bayesian semiparametric modeling of survival data based on mixtures of B-spline distributions," Computational Statistics & Data Analysis, Elsevier, vol. 55(3), pages 1260-1272, March.
    17. Björn Bornkamp & Katja Ickstadt, 2009. "Bayesian Nonparametric Estimation of Continuous Monotone Functions with Applications to Dose–Response Analysis," Biometrics, The International Biometric Society, vol. 65(1), pages 198-205, March.
    18. Mary Meyer & Amber Hackstadt & Jennifer Hoeting, 2011. "Bayesian estimation and inference for generalised partial linear models using shape-restricted splines," Journal of Nonparametric Statistics, Taylor & Francis Journals, vol. 23(4), pages 867-884.
    19. Alexandre Leblanc, 2012. "On estimating distribution functions using Bernstein polynomials," Annals of the Institute of Statistical Mathematics, Springer;The Institute of Statistical Mathematics, vol. 64(5), pages 919-943, October.
    20. Tenreiro, Carlos, 2003. "On the asymptotic normality of multistage integrated density derivatives kernel estimators," Statistics & Probability Letters, Elsevier, vol. 64(3), pages 311-322, September.
    21. Y. K. Tseng & Y. R. Su & M. Mao & J. L. Wang, 2015. "An extended hazard model with longitudinal covariates," Biometrika, Biometrika Trust, vol. 102(1), pages 135-150.

    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:spr:stpapr:v:59:y:2018:i:1:d:10.1007_s00362-016-0756-9. 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: Sonal Shukla or Springer Nature Abstracting and Indexing (email available below). General contact details of provider: http://www.springer.com .

    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.