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Books and Other Monographs

For Experts:

  • Besse, P. (1979) Etude descriptive des processus: Approximation et interpolation. Thèse de troisième cycle, Université Paul-Sabatier, Toulouse.
    I first learned about FDA from reading Philippe's doctoral dissertation in 1981. Statistics from a functional analytic perspective, it drew heavily from the path-breaking work of Dauxois and Pousse (1975). Hard to get, and you have to read French, but worth the trouble. Philippe has published a great deal of FDA research since, and also has supervised many fine theses.
  • Coddington, E. A. (1989) An Introduction to Ordinary Differential Equations. New York: Dover.
  • Coddington, E. A. and Levinson, N. (1955) Theory of Ordinary Differential Equations. New York: McGraw-Hill.
    These two books by Coddington are my favorites on ODE's.
  • Dauxois, J. and Pousse, A. (1976) Les analyses factorielles en calcul des probabilité et en statistique: Essai d'étude synthètique. Thèse d'état, Université Paul-Sabatier, Toulouse.
    When this joint work appeared, the earth moved. Gently and only locally at first, but the impact of this work is both nearly invisible and at the same enormous. See Philippe Besse's thesis, for example. Jacques Dauxois is still active at l'Université Mireil in Toulouse, but Alain Pousse has retired from l'Université de Pau. A group at Toulouse has just completed a large book on the use of functional analysis in statistics in English, and is in the process of publishing it, after over a quarter of a century.
  • de Boor, C. (2002) A Practical Guide to Splines. New York: Springer.
    This is a second edition of the 1979 classic on splines. A lot of detail, and written for researchers in numerical analysis, it is definitely for experts. But it is practical, too, and contains computer code that has been translated into many languages, including Matlab, where it is the backbone of spline computer toolbox.
  • Fan, J. and Gijbels, I. (1996) Local Polynomial Modelling and its Applications. London: Chapman and Hall.
    A comprehensive treatment of local polynomial smoothing.
  • Green, P. J. and Silverman, B. W. (1994) Nonparametric Regression and Generalized Linear Models: A Roughness Penalty Approach. London: Chapman and Hall.
    A comprehensive treatment of the use of roughness penalties in smoothing data and functional parameters.
  • Grenander, U. (1981) Abstract Inference. New York: Wiley.
    No list of books on statistics and functional data with a functional analytic orientation is complete without this. Full of interesting ideas that have yet to be fully explored. One reviewer of our book appropriately commented that this was really the first book FDA.
  • Schumaker, L. (1981) Spline Functions: Basic Theory. New York: Wiley.
    A classic work on the theory underlying spline functions, and especially important to me for what I learned about Green's functions and splines.
  • Silverman, B. W. (1986) Density Estimation. London: Chapman and Hall.
    A book widely admired for its clarity and style as well as its technical achievements. A density function is an example of a functional parameter that is estimated from a sample of scalar data.
  • Wahba, G. (1990) Spline Models for Observational Data. Philadelphia: Society for Industrial and Applied Mathematics.
    Listed here mostly to warn you that this is a difficult book, even though it is widely cited (and seldom read.)