Chapter 4: Beyond Linear Regression: The Method of Maximum Likelihood

  • Peter K. Dunn
  • Gordon K. Smyth
Part of the Springer Texts in Statistics book series (STS)


The linear regression model introduced in Chap.  2 assumes the variance is constant, possibly from a normal distribution.


  1. [1]
    Akaike, H.: A new look at the statistical model identification. IEEE Transactions on Automatic Control 19(6), 716–723 (1974)MathSciNetCrossRefGoogle Scholar
  2. [2]
    Box, G.E.P.: Science and statistics. Journal of the American Statistical Association 71, 791–799 (1976)MathSciNetCrossRefGoogle Scholar
  3. [3]
    Chatterjee, S., Handcock, M.S., Simonoff, J.S.: A Casebook for a First Course in Statistics and Data Analysis. John Wiley and Sons, New York (1995)zbMATHGoogle Scholar
  4. [4]
    Dala, S.R., Fowlkes, E.B., Hoadley, B.: Risk analysis of the space shuttle: pre-Challenger prediction of failure. Journal of the American Statistical Association 84(408), 945–957 (1989)Google Scholar
  5. [5]
    Dunn, P.K., Smyth, G.K.: Randomized quantile residuals. Journal of Computational and Graphical Statistics 5(3), 236–244 (1996)Google Scholar
  6. [6]
    Feigl, P., Zelen, M.: Estimation of exponential survival probabilities with concomitant information. Biometrics 21, 826–838 (1965)CrossRefGoogle Scholar
  7. [7]
    Glaister, D.H., Miller, N.L.: Cerebral tissue oxygen status and psychomotor performance during lower body negative pressure (LBNP). Aviation, Space and Environmental Medicine 61(2), 99–105 (1990)Google Scholar
  8. [8]
    Hauck Jr., W.W., Donner, A.: Wald’s test as applied to hypotheses in logit analysis. Journal of the American Statistical Association 72, 851–853 (1977)MathSciNetzbMATHGoogle Scholar
  9. [9]
    Maron, M.: Threshold effect of eucalypt density on an aggressive avian competitor. Biological Conservation 136, 100–107 (2007)CrossRefGoogle Scholar
  10. [10]
    McBride, J.L., Nicholls, N.: Seasonal relationships between Australian rainfall and the southern oscillation. Monthly Weather Review 111(10), 1998–2004 (1983)CrossRefGoogle Scholar
  11. [11]
    Montgomery, D.C., Peck, E.A.: Introduction to Regression Analysis. Wiley, New York (1992)zbMATHGoogle Scholar
  12. [12]
    Pook, M., Lisson, S., Risbey, J., Ummenhofer, C.C., McIntosh, P., Rebbeck, M.: The autumn break for cropping in southeast Australia: trends, synoptic influences and impacts on wheat yield. International Journal of Climatology 29, 2012–2026 (2009)CrossRefGoogle Scholar
  13. [13]
    Smyth, G.K.: Australasian data and story library (Ozdasl) (2011). URL
  14. [14]
    Stone, R.C., Auliciems, A.: soi phase relationships with rainfall in eastern Australia. International Journal of Climatology 12, 625–636 (1992)CrossRefGoogle Scholar

Copyright information

© Springer Science+Business Media, LLC, part of Springer Nature 2018

Authors and Affiliations

  • Peter K. Dunn
    • 1
  • Gordon K. Smyth
    • 2
  1. 1.Faculty of Science, Health, Education and EngineeringSchool of Health of Sport Science, University of the Sunshine CoastQueenslandAustralia
  2. 2.Bioinformatics DivisionWalter and Eliza Hall Institute of Medical ResearchParkvilleAustralia

Personalised recommendations