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For Intermediates:

  • Besse, P. and Ramsay, J. O. (1986) Principal components analysis of sampled functions. Psychometrika, 51, 285-311.
    Our first serious foray into FDA.
  • Castro, P. E., Lawton, W. H. and Sylvestre, E. A. (1986) Principal modes of variation for processes with continuous sample curves. Technometrics, 28, 329-337.
    An early approach to functional PCA.
  • Cleveland, W. S. (1979) Robust locally weighted regression and smoothing scatterplots. Journal of the American Statistical Association, 74, 829-836.
    The first paper on local polynomial smoothing.
  • Cressie, N. (1991) Statistics for Spatial Data. New York: Wiley.
    This and its second edition are the standard references on the statistical analysis of spatially distributed data.
  • Ramsay, J. O. (1982). When the data are functions. Psychometrika, 47, 379-396.
    This was my presidential address to the Psychometric Society in 1982. A little functional analysis for dummies! But it was a good start.
  • Ramsay, J. O. (2000). Functional components of variation in handwriting. Journal of the American Statistical Association, 95, 9-15.
    A remarkable fit to some complex functional data achieved by estimating a second order linear differential equation.
  • Ramsay, J. O. (2000). Differential equation models for statistical functions. Canadian Journal of Statistics. 28, 225-240.
    This surveys a number of ways in which differential equations can be used to define solutions to statistical problems. Watch out for the typo caused by omitting the "" from "exp".
  • Ramsay, J. O. and Ramsey, J. B. (2001) Functional data analysis of the dynamics of the monthly index of non durable goods production. Journal of Econometrics, 107, 327-344.
    Here we put the idea of phase-plane plotting to work to show temporal evolution of seasonal effects in this important economic index. Jim Ramsey is in the Department of Economics at New York University.
  • Rao, C. R. (1958) Some statistical methods for comparison of growth curves. Biometrics, 14, 1-17.
    One of the two first papers to explicitly consider functional data as a special type of data, and to adapt principal components analysis to the problem. See Tucker for the other.
  • Rossi, N., Wang, X., and Ramsay, J. O. (2002). Nonparametric item response function estimates with the EM algorithm. Journal of the Behavioral and Educational Sciences, 27, 291-317.
    FDA to work in the analysis of testing data, where item response functions are functional parameters used to describe binary or categorical data. This paper won the 2002 Technical Award of the National Council for Measurement in Education.
  • Shepstone, L., Rogers, J., Kirwan, J., and Silverman, B. W. (1999). The shape of the distal femur: A palaeopathological comparison of eburnated and non-eburnated femora. Annals of the Rheumatic Diseases, 58, 72-78.
  • Shepstone, L., Rogers, J., Kirwan, J., and Silverman, B. W. (2001). The shape of the intercondylar notch of the human femur: A comparison of osteoarthritic and non-osteoarthritic bones from a skeletal sample. Annals of the Rheumatic Diseases, 60, 968-973.
    These two papers put FDA tools to work on an interesting spatial data set.
  • Tucker, L. R. (1958) Determination of parameters of a functional relationship by factor analysis. Psychometrika, 23, 19-23.
    Here's the other classic to go along with Rao's paper. Exciting to think that this all happened in psychometrics, as so many other things did, too. I'm proud to be one of them.
  • Whittaker, E. (1923). On a new method of graduation. Proceedings of the Edinburgh Mathematical Society, 41, 63-75.
    Just to indicate how far back FDA goes!