Stat 500 - Fall 2007 - Dr. Philip Dixon

This page contains references in case you are interested in learning more about certain topics in this course. None of these are required. Required readings are here.

• Bootstrap and Randomization tests:
  • Information:
    • Preprint on bootstrapping, emphasizing environmental applications. (a .pdf file)
    • Chernick, M. R. 1999. Bootstrap Methods: A practioner's guide. Wiley. An overview with lots of references to theory and use.
    • Davison, A.C. and Hinkley, D. V. 1997. Bootstrap Methods and their Application. Cambridge Univ. Press. A comprehensive treatment of theory and practice. My favorite of the many bootstrap books.
    • Good, P. 2004. Permutation, Parametric, and Bootstrap Tests of Hypotheses. Springer. N.B. Previous editions had different titles. Nice overview of randomization tests. Latest edition (2007?) adds a second author.
  • Comparison to model based methods
    • Ludbrook and Dudley, 1998. Why permutation tests are superior to t- and F-tests in biomedical research. Am. Stat. 52:127-132.
    • Berger, V. 2000. Pros and cons of permutation tests in clinical trials. Statistics in Medicine 19:1319-1328.
    • Kempthorne, O. 1955. The randomization theory of experimental inference. Journal of the American Statistical Association 50: 946-967. Careful theoretical argument, but not light bedtime reading.
• Strengthening conclusions from observational data
  • Chapter 24, Statistical Evidence and Inference in Hill, A.B. 1977. A short textbook of medical statistics. Hodder and Stoughton, London. A non-technical discussion of various study characteristics that help make causal claims from observational studies.
  • Wang, C. 1993. Sense and Nonsense of Statistical Inference. Marcel Dekker, New York. A non-technical critique of the widespread use of statistical methods to make strong claims from observational data.
  • Rosenbaum, P. Observational Studies. Springer. A technical and rigorous treatment.
  • Pearl, J. Causality: Models, Reasoning and Inference. Cambridge Univ. Press. A more philosophical treatment of causation and models, especially graphical models, for how to compare different putative causal mechanisms.

• Diagnostics
  • Madansky, A. 1988. Prescriptions for Working Statisticians. Springer. A catalog of methods to assess assumptions, with technical details.
  • Miller, R.G. Jr. 1986. Beyond ANOVA, Basics of Applied Statistics. Wiley. An intermediate level treatment of assumptions, diagnoses, and consequences.
  • Box, G.E.P. 1953. Non-normality and test on variances. Biometrika 40:318-335. The classic investigation of the robustness to non-normality.
  • Conover, W.J., Johnson, M.E. and Johnson, M.M. 1981. A comparative study of tests for homogeneity of variances, with applications to the outer continental shelf bidding data. Technometrics 23:351-361. Extensive similation evaluation of F tests, Levene's tests and variants.
  • Pearson, E.S., Please N.Ww. 1975. Relation between shape of population distribution and robustness of 4 simple test statistics. Biometrika 62: 223-241. Extensive simulation evaluation of non-normality.

• Multiple comparisons
  • Hsu, J.C. 1996. Multiple comparisons: theory and methods. Chapman and Hall/CRC. A good intermediate level text on many methods. Chapter 6 (pp 175-180) is full of good, useful advice.
  • Example where adjusting or not adjusting leads to very different policy, Women's Health Initiative study of long duration ostrogen: Discussed in Science (26 July 2002) 297:492. Two similar studies of risk and benefits of long term estrogen replacement therapy. One study is terminated early because one comparison indicates increased risk to participants. Simultaneous confidence intervals indicate no evidence of increased risk. Other study continued.
  • Two papers from agricultural literature illustrating the diversity of opinions:
    Carmer, S.G. and Walker, W.M. 1982. Baby bear's dilemma: a statistical tale. Agronomy Journal 74:122-124.
    Argues for never using m.c.p. (i.e. always using l.s.d.) because it provides highest power.

    Peterson, R.G. 1977. Use and misuse of multiple comparison procedures. Agronomy Journal 69:205-208.
    Recommends m.c.p. when 'data snooping', i.e. when looking for interesting patterns. m.c.p. are 'almost never appropriate' for quantitative treatments, factorial treatment structures, and answering specific questions.

• History of regression
  • Galton's paper on parent-child relationships is Galton, F. 1886. Regression towards mediocrity in hereditary stature. Journal of the Anthropological Institute of Great Britain and Ireland 15:246-263. It's availabile online through JSTOR (www.jstor.org). The figures I showed in lecture came from this. An appendix also has some of the sweet pea data.
  • Galton's 1877 sweet pea is apparently published in Galton, F. 1877. Typical laws of heredity. Nature 15:492-495, 512-514, 532-533, but I haven't seen these yet.
  • A detailed history of Galton's contributions with a translation into modern statistical concepts is pp 265-299 in Stigler, S. M. 1986. The History of Statistics: the measurement of uncertainty before 1900. Belknap Press, Boston MA.

• Regression with measurement errors
  • Berkson, J.\ 1950. Are there two regressions? J. Am. Stat. Assoc. 45:164-180.
  • Fuller, W.A.\ 1987. Measurement Error Models. Wiley.
    The first chapter is an overview of the effects of measurement error in simple linear regression. The rest of the book covers more complicated situations.

• Ridge regression and Regularization/Shrinkage methods (eg. LASSO), focusing on applications with very large number of X variables.
  • Textbook review: section 3.4.3 (pp 59-65) in Hastie, T., Tibshirani, R. and Friedman, J. 2001. The Elements of Statistical Learning. sections 3.4.4 and 3.4.5 (pp 66 - 72) discribe then compare other approaches to multicollinearity.
  • Ghosh, D. 2003. Penalized Discriminant Methods for the Classification of Tumors from Gene Expression Data. Biometrics 52:992-1000.
    Application of regression to produce a classification, using ridge regression and other methods with many X variables.
• Model selection issues
  • Burnham, K. P. and Anderson, D.R. 1998. Model Selection and Inference, a practical information-theoretic approach. (now in 2nd ed., ca 2004?).
    AIC based model selection from an applied frequentist perspective. Has lots of examples, mostly ecological, but doesn't shy away from AIC theory.
  • Hoeting JA, Madigan D, Raftery AE, et al. 1999. Bayesian model averaging: A tutorial. Statistical Science 14: 382-401.
    Adrian Raftery's group has been very active in understanding inference when the model is not clear. This is an overview paper on the Bayesian approach.
  • Raftery AE 1995. Bayesian model selection in social research Sociological Methodology 25: 111-163
    And this is a review in the sociological literature.
  • Harrell, F. 2001. Regression Modeling Strategies. Springer.
    There are many texts on regression. This is by far my favorite. Great coverage of traditional regression, model selection, model validation, along with logistic regression (0/1 response) and Poisson regression (count response).