Journals

For Experts:

• Anselone, P. M. and Laurent, P. J. (1967) A general method for the construction of interpolating or smoothing spline-functions. Numerische Mathematik, 12, 66-82.
  A classic paper on smoothing splines from the Golden Age of spline research by two pioneers. You need some functional analysis to read this, but it's one of my all-time favorites.
• Ansley, C. F., Kohn, R. and Wong, C-M. (1993) Nonparametric spline regression with prior information. Biometrika, 80, 75-88.
  Smoothing splines can be computed using the Kalman Filter, and also generalized in this way. These authors show us how to some extent, but this great work never resulted in useable computer code.
• Brumback, B. A. and Rice, J. (1998) Smoothing spline models for the analysis of nested and crossed samples of curves. Journal of the American Statistical Association, 93, 961-976.
  This is a discussed paper in JASA, and illustrates some of the challenges involved in melding longitudinal data and FDA approaches, most notably the problem of representing between-replicate variation when the observations are high dimensional. This problem needs more study.
• Craven, P. and Wahba, G. (1979) Smoothing noisy data with spline functions: estimating the correct degree of smoothing by the method of generalized cross-validation, Numerische Mathematik, 31, 377-403.
  A classic paper on data smoothing with splines, where the important method of generalized cross-validation was introduced for selecting a smoothing parameter value.
• Dauxois, J., Pousse, A. and Romain, Y. (1982) Asymptotic theory for the principal component analysis of a vector random function: some applications to statistical inference. Journal of Multivariate Analysis, 12, 136-154.
  A publication coming out of the Dauxois-Pousse thesis. Exceedingly difficult to read, but nevertheless important. Yves Romain is still at l'Université Paul Sabatier in Toulouse, where he is perhaps the world's leading expert on the use of operator algebra to tackle statistical problems.
• Deville, J. C. (1974) Méthodes statistiques et numériques de l'analyse harmonique. Annales de l'INSEE, 15, 7-97.
  An outstanding very early work on FDA in the French literature. Jean-Claude had the vision!
• Gasser, T. and Kneip, A. (1995). Searching for structure in curve samples. Journal of the American Statistical Association, 90, 1179-1188.
  Two pioneers in curve registration explain the problem and provide some useful solutions using landmarks.
• Hall, P and Heckman, N. E. (2002) Estimating and depicting the structure of a set of random functions. Biometrika, 89, 145-158.
  An innovative approach to thinking about the distribution of functional objects.
• Hastie, T. and Tibshirani, R. (1993). Varying-coefficient models. Journal of the Royal Statistical Society, Series B, 55, 757-796.
  We inexcusably neglected this seminal work on the pointwise functional linear model.
• Heckman, N. E. and Ramsay, J. O. (2000). Penalized regression with model based penalties. Canadian Journal of Statistics, 28, 241-258.
  The notion of a roughness penalty is extended here to permit the use of any linear differential operator. This also implies an generalization of B-splines to basis functions that, like B-splines, have support only over a small number intervals, but can be piecewise linear combinations of any functions spanning the null space of the operator. This work has important implications for the problem of estimating differential equations from data, a topic that is currently being researched. The paper won the Best Paper in the CJS award by the Statistical Society of Canada for the year.
• James, G. (2002) Generalized linear models with functional predictor variables, Journal of the Royal Statistical Society, Series B, 64, 411-432.
  Gareth James is a new researcher who has left the starting gate with remarkable speed and power. This paper generalizes the functional independent variable situation to a much wider range of dependent variables than was considered in our books.
• James, G., and Hastie, T. (2001) Functional linear discriminant analysis for irregularly sampled curves, Journal of the Royal Statistical Society, Series B, 63, 533-550.
• James, G., Hastie, T., and Sugar, C. (2000) Principal component models for sparse functional data", Biometrika, 87, 587-602.
  Often replicated functional observations do not all have the same intervals over which measurements are taken. This is especially true of longitudinal studies of children, where keeping a subject in a study over a long and fixed period is extremely expensive and difficult. These papers report an important extension of FDA technology.
• Kimeldorf, G. S. and Wahba, G. (1970) A correspondence between Bayesian estimation on stochastic processes and smoothing by splines. Annals of Mathematical Statistics, 41, 495-502.
  An often-cited paper explaining how spline smoothing can be viewed as a functional Bayesian estimation problem.
• Kneip, A., Li, X., MacGibbon, B., and Ramsay, J. O. (2000). Curve registration by local regression. Canadian Journal of Statistics, 28, 19-30.
  Another approach to continuous curve regression that works well, and has since been adapted to two-dimensional neuro-images by Florence Nicol in her thesis at l'Université Catholique de Louvain-la-Neuve.
• Leurgans, S. E., Moyeed, R. A. and Silverman, B. W. (1993) Canonical correlation analysis when the data are curves. Journal of the Royal Statistical Society, Series B, 55, 725-740.
  The original paper on canonical correlation analysis in a functional context.
• Malfait, N., Ramsay, J. O., and Froda, S. (2001). The historical functional linear model. The Canadian Journal of Statistics, to appear.
  This paper uses finite element methods to fit a functional linear model integrating information in a covariate over times up to the present and back a fixed distance.
• Ramsay, J. O. (1996b). Principal differential analysis: Data reduction by differential operators. Journal of the Royal Statistical Society, Series B, 58, 495-508. The first paper on estimating differential equations to model functional data.
• Ramsay, J. O. (1998). Estimating smooth monotone functions. Journal of the Royal Statistical Society, Series B, 60, 365-375.
  By defining a monotone function as a solution to a differential equation, a new and powerful monotone smoothing method was developed.
• Ramsay, T. O. (2002) Spline smoothing over difficult regions. Journal of the Royal Statistical Society, Series B, 64, 307-319.
  This is only a representative of a large literature on smoothing over two-dimensional images, but important in that it recognizes that special measures are required with the boundaries of the region are complex, rather than just rectangular. It also uses finite elements rather than radial basis functions. Finally, it formulates the smoothing problem as the solution to a partial differential equation. T. Ramsay is also related to one of the FDA authors, who clearly has no shame!
• Ramsay, J. O. and Dalzell, C. J. (1991) Some tools for functional data analysis (with Discussion). Journal of the Royal Statistical Society, Series B, 53, 539-572.
  The paper where the term "functional data analysis" was first used, and some of the basic theory was set out. The discussions in these RSS read papers are worth as much as the main article.
• Ramsay, J. O. and Li, X. (1996) Curve registration. Journal of the Royal Statistical Society, Series B., 60, 351 363.
  The problem of curve registration using the entire curve rather than just landmarks is considered here. We subsequently abandoned the least squares criterion in favor of something better.
• Rice, J. A. and Silverman, B. W. (1991) Estimating the mean and covariance structure nonparametrically when the data are curves. Journal of the Royal Statistical Society, Series B, 53, 233-243.
  A first paper proposing smoothing in functional PCA.
• Silverman, B. W. (1995). Incorporating parametric effects into functional principal components analysis. Journal of the Royal Statistical Society, Series B, 57, 673-689.
  Here Bernard describes a hybrid form of PCA that permits the study of joint variation in multivariate and functional variables.
• Silverman, B. W. (1996). Smoothed functional principal components analysis by choice of norm. Annals of Statistics, 24, 1-24.
  This is an improvement on the work of Rice and Silverman by the introduction of a better method of smoothing eigenfunctions.