Statistical inference and visualization in scale-space using local likelihood
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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Volume (Year): 57 (2013)
Issue (Month): 1 ()
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- Ruppert,David & Wand,M. P. & Carroll,R. J., 2003. "Semiparametric Regression," Cambridge Books, Cambridge University Press, number 9780521785167, December.
- 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.
- Huh, Jib, 2010. "Detection of a change point based on local-likelihood," Journal of Multivariate Analysis, Elsevier, vol. 101(7), pages 1681-1700, August.
- Ruppert,David & Wand,M. P. & Carroll,R. J., 2003. "Semiparametric Regression," Cambridge Books, Cambridge University Press, number 9780521780506, December.
- Pollard, David, 1991. "Asymptotics for Least Absolute Deviation Regression Estimators," Econometric Theory, Cambridge University Press, vol. 7(02), pages 186-199, June.
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