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Statistical inference and visualization in scale-space using local likelihood

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  • Park, Cheolwoo
  • Huh, Jib
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    Abstract

    SiZer (SIgnificant ZERo crossing of the derivatives) is a graphical scale-space visualization tool that allows for exploratory data analysis with statistical inference. Various SiZer tools have been developed in the last decade, but most of them are not appropriate when the response variable takes discrete values. In this paper, we develop a SiZer for finding significant features using a local likelihood approach with local polynomial estimators. This tool improves the existing one (Li and Marron, 2005) by proposing a theoretically justified quantile in a confidence interval using advanced distribution theory. In addition, we investigate the asymptotic properties of the proposed tool. We conduct a numerical study to demonstrate the sample performance of SiZer using Bernoulli and Poisson models using simulated and real examples.

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    Bibliographic Info

    Article provided by Elsevier in its journal Computational Statistics & Data Analysis.

    Volume (Year): 57 (2013)
    Issue (Month): 1 ()
    Pages: 336-348

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    Handle: RePEc:eee:csdana:v:57:y:2013:i:1:p:336-348

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    Web page: http://www.elsevier.com/locate/csda

    Related research

    Keywords: Generalized linear models; Local likelihood; Local polynomial smoothing; Scale-space; Statistical significance;

    References

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    Please report citation or reference errors to , or , if you are the registered author of the cited work, log in to your RePEc Author Service profile, click on "citations" and make appropriate adjustments.:
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    1. Ruppert,David & Wand,M. P. & Carroll,R. J., 2003. "Semiparametric Regression," Cambridge Books, Cambridge University Press, number 9780521780506, April.
    2. Huh, J. & Park, B. U., 2002. "Likelihood-Based Local Polynomial Fitting for Single-Index Models," Journal of Multivariate Analysis, Elsevier, vol. 80(2), pages 302-321, February.
    3. Cheolwoo Park & J. S. Marron & Vitaliana Rondonotti, 2004. "Dependent SiZer: Goodness-of-Fit Tests for Time Series Models," Journal of Applied Statistics, Taylor & Francis Journals, vol. 31(8), pages 999-1017.
    4. Ruppert,David & Wand,M. P. & Carroll,R. J., 2003. "Semiparametric Regression," Cambridge Books, Cambridge University Press, number 9780521785167, April.
    5. Sørbye, Sigrunn H. & Hindberg, Kristian & Olsen, Lena R. & Rue, Håvard, 2009. "Bayesian multiscale feature detection of log-spectral densities," Computational Statistics & Data Analysis, Elsevier, vol. 53(11), pages 3746-3754, September.
    6. Hannig, J. & Marron, J.S., 2006. "Advanced Distribution Theory for SiZer," Journal of the American Statistical Association, American Statistical Association, vol. 101, pages 484-499, June.
    7. Godtliebsen, Fred & Oigard, Tor Arne, 2005. "A visual display device for significant features in complicated signals," Computational Statistics & Data Analysis, Elsevier, vol. 48(2), pages 317-343, February.
    8. Pollard, David, 1991. "Asymptotics for Least Absolute Deviation Regression Estimators," Econometric Theory, Cambridge University Press, vol. 7(02), pages 186-199, June.
    9. Oigard, Tor Arne & Rue, Havard & Godtliebsen, Fred, 2006. "Bayesian multiscale analysis for time series data," Computational Statistics & Data Analysis, Elsevier, vol. 51(3), pages 1719-1730, December.
    10. Park, Cheolwoo & Kang, Kee-Hoon, 2008. "SiZer analysis for the comparison of regression curves," Computational Statistics & Data Analysis, Elsevier, vol. 52(8), pages 3954-3970, April.
    11. Huh, Jib, 2010. "Detection of a change point based on local-likelihood," Journal of Multivariate Analysis, Elsevier, vol. 101(7), pages 1681-1700, August.
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