Second-derivative functional regression with applications to near infra-red spectroscopy

Journal of the Royal Statistical Society. Series B: Statistical Methodology

Volumn 60, Issue 1, 1998, Pages 103-114

  Goutis, Constantinos ^a  

^a UNIVERSIDAD CARLOS III DE MADRID   (Spain)

Author keywords

Calibration; Chemometrics; Cross validation; Differential operator; Nonparametric derivative estimation; Roughness penalty

Indexed keywords

EID: 0000590738     PISSN: 13697412     EISSN: None     Source Type: Journal    
DOI: 10.1111/1467-9868.00111     Document Type: Article

References (29)

1. Alsberg, B. J. (1993) Representation of spectra by continuous functions. J. Chemometr., 7, 177-193.
2. Anderssen, R. S. and Bloomfield, P. (1974) A time series approach to numerical differentiation. Technometrics, 16, 69-75.
3. Besse, P. and Ramsay, J. O. (1986) Principal components analysis of sampled functions. Psychometrika, 51, 285-311.
4. Brown, P. J. (1982) Multivariate calibration (with discussion). J. R. Statist. Soc. B, 44, 287-321.
5. _ (1993) Measurement, Regression, and Calibration. Oxford: Clarendon.
6. Denham, M. C. and Brown, P. J. (1993) Calibration with many variables. Appl. Statist., 42, 515-528.
7. Dunne, T. T. and Stone, M. (1993) Downdating the Moore-Penrose generalized inverse for cross-validation of centred least squares prediction. J. R. Statist. Soc. B, 55, 369-375.
8. Frank, I. E. and Friedman, J. H. (1993) A statistical view of some chemometrics regression tools (with discussion). Technometrics, 35, 109-147.
9. Gasser, T. and Müller, H.-G. (1984) Estimating regression functions and their derivatives by the kernel method. Scand. J. Statist., 11, 171-185.
10. Gasser, T., Müller, H.-G., Köhler, W., Molinari, L. and Prader, A. (1984) Nonparametric regression analysis of growth curves. Am. Statist., 12, 210-229.
11. Gasser, T., Müller, H.-G. and Mammitzsch, V. (1985) Kernels for nonparametric curve estimation. J. R. Statist. Soc. B, 47, 238-252.
12. Gorry, P. A. (1990) General least-squares smoothing and differentiation by the convolution (Savitzky-Golay) method. Anal. Chem., 62, 570-573.
13. _ (1991) General least-squares smoothing and differentiation of nonuniformly spaced data by the convolution method. Anal Chem., 63, 534-536.
14. Goutis, C. and Fearn, T. (1996) Partial least squares regression on smooth factors. J. Am. Statist. Ass., 91, 627-633.
15. Green, P. J. and Silverman, B. W. (1994) Nonparametric Regression and Generalised Linear Models; a Roughness Penalty Approach. London: Chapman and Hall.
16. Hastie, T., Buja, A. and Tibshirani, R. (1995) Penalized discriminant analysis. Ann. Statist., 23, 73-102.
17. Hastie, T. and Mallows, C. (1993) Comment on "A statistical view of some chemometrics regression tools" by I. E. Frank and J. H. Friedman. Technometrics, 35, 140-143.
18. Martens, H. and Næs, T. (1989) Multivariate Calibration. New York: Wiley.
19. Müller, H.-G. (1988) Nonparametric regression analysis of longitudinal data. Lect. Notes Statist., 46.
20. Müller, H.-G., Stadtmüller, U. and Schmitt, T. (1987) Bandwidth choice and confidence intervals for derivatives of noisy data. Biometrika, 74, 743-749.
21. Norris, K. H. (1983) Extracting information from spectrophotometric curves: predicting chemical composition from visible and near infrared spectra. In Food Research and Data Analysis (eds H. Martens and H. Russwurm, Jr), pp. 95-113. London: Applied Science Publishers.
22. Osborne, B. G., Fearn, T. and Kindle, P. H. (1993) Practical NIR Spectroscopy, 2nd edn. Harlow: Longman.
23. Ramsay, J. O., Altman, N. and Bock, R. D. (1994) Variation in height acceleration in the Fels growth data. Can. J. Statist., 22, 89-102.
24. Ramsay, J. O. and Dalzell, C. J. (1991) Some tools for functional data analysis (with discussion). J. R. Statist. Soc. B, 53, 539-572.
25. Ramsay, J. O., Wang, X. and Flanagan, R. (1995) A functional data analysis of the pinch force of human fingers. Appl. Statist., 44, 17-30.
26. Rice, J. (1984) Bandwidth choice for nonparametric regression. Ann. Statist., 12, 1215-1230.
27. Rice, J. A. and Silverman, B. W. (1991) Estimating the mean and covariance structure nonparametrically when the data are curves. J. R. Statist. Soc. B, 53, 233-243.
28. Savitzky, A. and Golay, M. J. E. (1964) Smoothing and differentiation of data by simplified least squares procedures. Anal. Chem., 36, 1627-1639.
29. Wahba, G. (1990) Spline Models for Observational Data. Philadelphia: Society for Industrial and Applied Mathematics.