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Density estimation and comparison with a penalized mixture approach

  • Christian Schellhase
  • Göran Kauermann

    ()

The paper presents smooth estimation of densities utilizing penalized splines. The idea is to represent the unknown density by a convex mixture of basis densities, where the weights are estimated in a penalized form. The proposed method extends the work of Komárek and Lesaffre (Comput Stat Data Anal 52(7):3441–3458, 2008 ) and allows for general density estimation. Simulations show a convincing performance in comparison to existing density estimation routines. The idea is extended to allow the density to depend on some (factorial) covariate. Assuming a binary group indicator, for instance, we can test on equality of the densities in the groups. This provides a smooth alternative to the classical Kolmogorov-Smirnov test or an Analysis of Variance and it shows stable and powerful behaviour. Copyright Springer-Verlag 2012

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File URL: http://hdl.handle.net/10.1007/s00180-011-0289-6
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Article provided by Springer in its journal Computational Statistics.

Volume (Year): 27 (2012)
Issue (Month): 4 (December)
Pages: 757-777

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Handle: RePEc:spr:compst:v:27:y:2012:i:4:p:757-777
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  1. Gilles Celeux & Gilda Soromenho, 1996. "An entropy criterion for assessing the number of clusters in a mixture model," Journal of Classification, Springer, vol. 13(2), pages 195-212, September.
  2. repec:cup:cbooks:9780521785167 is not listed on IDEAS
  3. repec:cup:cbooks:9780521780506 is not listed on IDEAS
  4. Tatiana Benaglia & Didier Chauveau & David R. Hunter & Derek S. Young, . "mixtools: An R Package for Analyzing Mixture Models," Journal of Statistical Software, American Statistical Association, vol. 32(i06).
  5. Gerda Claeskens & Tatyana Krivobokova & Jean D. Opsomer, 2009. "Asymptotic properties of penalized spline estimators," Biometrika, Biometrika Trust, vol. 96(3), pages 529-544.
  6. Philip T. Reiss & R. Todd Ogden, 2009. "Smoothing parameter selection for a class of semiparametric linear models," Journal of the Royal Statistical Society Series B, Royal Statistical Society, vol. 71(2), pages 505-523.
  7. Göran Kauermann & Tatyana Krivobokova & Ludwig Fahrmeir, 2009. "Some asymptotic results on generalized penalized spline smoothing," Journal of the Royal Statistical Society Series B, Royal Statistical Society, vol. 71(2), pages 487-503.
  8. Yingxing Li & David Ruppert, 2008. "On the asymptotics of penalized splines," Biometrika, Biometrika Trust, vol. 95(2), pages 415-436.
  9. H�vard Rue & Sara Martino & Nicolas Chopin, 2009. "Approximate Bayesian inference for latent Gaussian models by using integrated nested Laplace approximations," Journal of the Royal Statistical Society Series B, Royal Statistical Society, vol. 71(2), pages 319-392.
  10. Simon N. Wood, 2011. "Fast stable restricted maximum likelihood and marginal likelihood estimation of semiparametric generalized linear models," Journal of the Royal Statistical Society Series B, Royal Statistical Society, vol. 73(1), pages 3-36, January.
  11. Komárek, Arnost & Lesaffre, Emmanuel, 2008. "Generalized linear mixed model with a penalized Gaussian mixture as a random effects distribution," Computational Statistics & Data Analysis, Elsevier, vol. 52(7), pages 3441-3458, March.
  12. Ja-Yong Koo, 1999. "Logspline Density Estimation under Censoring and Truncation," Scandinavian Journal of Statistics, Danish Society for Theoretical Statistics;Finnish Statistical Society;Norwegian Statistical Association;Swedish Statistical Association, vol. 26(1), pages 87-105.
  13. Göran Kauermann & Jean D. Opsomer, 2011. "Data-driven selection of the spline dimension in penalized spline regression," Biometrika, Biometrika Trust, vol. 98(1), pages 225-230.
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