Functional data analysis with increasing number of projections

Journal of Multivariate Analysis

Volumn 124, Issue , 2014, Pages 313-332

  Fremdt, Stefan ^a   Horváth, Lajos ^b   Kokoszka, Piotr ^c   Steinebach, Josef G ^d  

^a RUHR UNIVERSITY BOCHUM   (Germany)

^b UNIVERSITY OF UTAH   (United States)

^c Veterinary Dentistry and Oral Surgery   (United States)

^d UNIVERSITY OF COLOGNE   (Germany)

Author keywords

Change in mean; Functional data; Increasing dimension; Normal approximation; Principal components

Indexed keywords

EID: 84890020547     PISSN: 0047259X     EISSN: 10957243     Source Type: Journal    
DOI: 10.1016/j.jmva.2013.11.009     Document Type: Article

References (31)

1. Aston J.A.D., Kirch C. Estimation of the distribution of change-points with application to fMRI data. Ann. Appl. Stat. 2012, 6:1906-1948.
2. Aue A., Hörmann S., Horváth L., Reimherr M. Break detection in the covariance structure of multivariate time series models. Ann. Statist. 2009, 37:4046-4087.
3. Basseville M., Nikifirov I.V., Tartakovsky A. Sequential Analysis: Hypothesis Testing and Change-Point Detection 2012, Chapman & Hall/CRC.
4. Bathia N., Yao Q., Ziegelmann F. Identifying the finite dimensionality of curve time series. Ann. Statist. 2010, 38:3353-3386.
5. Benko M., Härdle W., Kneip A. Common functional principal components. Ann. Statist. 2009, 37:1-34.
6. Berkes I., Gabrys R., Horváth L., Kokoszka P. Detecting changes in the mean of functional observations. J. R. Stat. Soc. Ser. B Stat. Methodol. 2009, 71:927-946.
7. Cardot H., Ferraty F., Mas A., Sarda P. Testing hypothesis in the functional linear model. Scand. J. Stat. 2003, 30:241-255.
8. Chen J., Gupta A.K. Parametric Statistical Change Point Analysis: With Applications to Genetics, Medicine, and Finance 2012, Birkhäuser. second ed.
9. Csörgo M., Horváth L. Limit Theorems in Change-Point Analysis 1997, Wiley, New York.
10. Csörgo M., Révész P. Strong Approximations in Probability and Statistics 1981, Academic Press, New York.
11. Dunford N., Schwartz J.T. Linear Operators, Parts I and II 1988, Wiley.
12. Einmahl U. Strong invariance principles for partial sums of independent random vectors. Ann. Probab. 1987, 15:1419-1440.
13. Einmahl U. Extension of results of Komlós, Major and Tusnady to the multivariate case. J. Multivariate Anal. 1989, 28:20-68.
14. Gallagher C., Lund R., Robbins M. Changepoint detection in daily precipitation data. Environmetrics 2012, 23:407-419.
15. 6th Berkeley Symp. Math. Stat. Probab. 1970, vol. 2:369-374. University of California Press.
16. Gohberg I., Golberg S., Kaashoek M.A. Operator Theory: Advances and Applications. Classes of Linear Operators 1990, vol. 49. Birkhaüser.
17. Gromenko O., Kokoszka P., Zhu L., Sojka J. Estimation and testing for spatially indexed curves with application to ionospheric and magnetic field trends. Ann. Appl. Stat. 2012, 6:669-696.
18. Hahn M.G. Central limit theorems in D [0, 1]. Z. Wahrscheinlichkeitstheor. Verwandte Geb. 1978, 44:89-101.
19. Hall P., Vial C. Assessing the finite dimensionality of functional data. J. R. Stat. Soc. Ser. B Stat. Methodol. 2006, 68:689-705.
20. Horváth L., Kokoszka P. Inference for Functional Data with Applications 2012, Springer.
21. Horváth L., Kokoszka P., Reeder R. Estimation of the mean of functional time series and a two sample problem. J. R. Stat. Soc. Ser. B Stat. Methodol. 2013, 75:103-122.
22. Horváth L., Kokoszka P., Reimherr M. Two sample inference in functional linear models. Canad. J. Statist. 2009, 37:571-591.
23. Howell J.O., Taylor R.L. Marcinkiewicz-Zygmund weak laws of large numbers for unconditional random elements in Banach spaces. Probability in Banach Spaces. III. Proceedings of the Third International Conference held at Tufts University, Medford, Mass. 1980, 219-230. Springer. J. Kuelbs (Ed.).
24. Kuelbs J. The invariance principle for Banach space valued random variables. J. Multivariate Anal. 1973, 3:161-172.
25. Panaretos V.M., Kraus D., Maddocks J.H. Second-order comparison of Gaussian random functions and the geometry of DNA minicircles. J. Amer. Statist. Assoc. 2010, 105:670-682.
26. Petrov V.V. Limit Theorems of Probability Theory: Sequences of Independent Random Variances 1995, Clarendon Press.
27. Ramsay J., Hooker G., Graves S. Functional Data Analysis with R and MATLAB 2009, Springer.
28. Ramsay J.O., Silverman B.W. Functional Data Analysis 2005, Springer.
29. Senatov V.V. Normal Approximation: New Results, Methods and Problems 1998, VSP.
30. Strassen V. The existence of probability measures with given marginals. Ann. Math. Stat. 1965, 36:423-439.
31. Woyczynski W. Geometry and martingales in Banach spaces. II. independent increments. Probability on Banach Spaces 1978, 267-517. Marcel Dekker. J. Kuelbs (Ed.).