Table of Contents
ISRN Probability and Statistics
Volume 2013, Article ID 496180, 22 pages
http://dx.doi.org/10.1155/2013/496180
Research Article

Linear Models with Response Functions Based on the Laplace Distribution: Statistical Formulae and Their Application to Epigenomics

1INMS, Massey University, Albany Campus, Private Bag 102-904, North Shore Mail Centre, Auckland 0745, New Zealand
2Liggins Institute, The University of Auckland, Private Bag 92019, Victoria Street West, Auckland 1142, New Zealand
3Gravida, National Centre for Growth and Development, The University of Auckland, Private Bag 92019, Victoria Street West, Auckland 1142, New Zealand
4Ruakara Research Centre, 10 Bisley Road, Private Bag 3115, Hamilton 3240, New Zealand

Received 20 June 2013; Accepted 24 July 2013

Academic Editors: A. A. Ding and J. López-Fidalgo

Copyright © 2013 C. Z. W. Hassell Sweatman et al. This is an open access article distributed under the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.

Linked References

  1. A. J. Dobson and A. G. Barnett, An Introduction to Generalized Linear Models, Chapman and Hall/CRC Press, 3rd edition, 2008.
  2. G. Bassett Jr. and R. Koenker, “Asymptotic theory of least absolute error regression,” Journal of the American Statistical Association, vol. 73, no. 363, pp. 618–622, 1978. View at Publisher · View at Google Scholar · View at MathSciNet
  3. D. Birkes and Y. Dodge, Alternative Methods of Regression, John Wiley & Sons, New York, NY, USA, 1993. View at Publisher · View at Google Scholar · View at MathSciNet
  4. P. Bloomfield and W. L. Steiger, Least Absolute Deviations, Theory Applications and Algorithms, Birkhäuser, Boston, Mass, USA, 1983. View at MathSciNet
  5. R. Koenker and G. Bassett, Jr., “Regression Quantiles,” Econometrica, vol. 46, no. 1, pp. 33–50, 1978. View at Publisher · View at Google Scholar · View at MathSciNet
  6. S. C. Narula and J. F. Wellington, “The minimum sum of absolute errors regression: a state of the art survey,” International Statistical Review, vol. 50, no. 3, pp. 317–326, 1982. View at Publisher · View at Google Scholar · View at MathSciNet
  7. R. M. Norton, “The double exponential distribution: using calculus to find a maximum likelihood estimator,” The American Statistician, vol. 38, no. 2, pp. 135–136, 1984. View at Google Scholar
  8. R. T. Rockafellar, Convex Analysis, Princeton University Press, Princeton, NJ, USA, 10th edition, 1970. View at MathSciNet
  9. M. J. Lighthill, Introduction to Fourier Analysis and Generalized Functions, Cambridge University Press, New York, NY, USA, 1958. View at MathSciNet
  10. I. Stakgold, Boundary Value Problems of Mathematical Physics, Vol. 1, The Macmillan, New York, NY, USA, 1967. View at MathSciNet
  11. E. L. Lehmann and G. Casella, Theory of Point Estimation, Springer, New York, NY, USA, 2nd edition, 1998. View at MathSciNet
  12. M. Ehrich, M. R. Nelson, P. Stanssens et al., “Quantitative high-throughput analysis of DNA methylation patterns by base-specific cleavage and mass spectrometry,” Proceedings of the National Academy of Sciences of the United States of America, vol. 102, no. 44, pp. 15785–15790, 2005. View at Publisher · View at Google Scholar · View at Scopus
  13. S. S. Shapiro and M. B. Wilk, “An analysis of variance test for normality: complete samples,” Biometrika, vol. 52, pp. 591–611, 1965. View at Google Scholar · View at MathSciNet
  14. S. T. Buckland, “Fitting density functions with polynomials,” Journal of the Royal Statistical Society Series C (Applied Statistics), vol. 41, no. 1, pp. 63–76, 1992. View at Publisher · View at Google Scholar · View at MathSciNet
  15. S. T. Buckland, “Maximum likelihood fitting of hermite and simple polynomial densities,” Journal of the Royal Statistical Society Series C (Applied Statistics), vol. 41, pp. 241–267, 1992. View at Google Scholar
  16. Pleasants, unpublished observations.
  17. W. Hendricks and R. Koenker, “Hierarchical spline models for conditional quantiles and the demand for electricity,” Journal of the American Statistical Association, vol. 87, no. 417, pp. 58–68, 1978. View at Google Scholar
  18. R. Koenker and G. Bassett, “Tests of linear hypotheses ond l1 estimation,” Econometrica, vol. 50, pp. 1157–1583, 1982. View at Google Scholar
  19. S. Kotz, T. J. Kozubowski, and K. Podgórski, The Laplace Distribution and Generalizations, Birkhäuser, Boston, Mass, USA, 2001. View at Publisher · View at Google Scholar · View at MathSciNet
  20. E. Purdom and S. P. Holmes, “Error distribution for gene expression data,” Statistical Applications in Genetics and Molecular Biology, vol. 4, no. 1, article 16, 2005. View at Publisher · View at Google Scholar · View at MathSciNet
  21. D. Kincaid and W. Cheney, Mathematics of Scientific Computing, Brooks/Cole, 3rd edition, 2002.