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On local times, density estimation and supervised classification from functional data

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  • Llop, P.
  • Forzani, L.
  • Fraiman, R.

Abstract

In this paper, we define a -consistent nonparametric estimator for the marginal density function of an order one stationary process built up from a sample of i.i.d continuous time trajectories. Under mild conditions we obtain strong consistency, strong orders of convergence and derive the asymptotic distribution of the estimator. We extend some of the results to the non-stationary case. We propose a nonparametric classification rule based on local times (occupation measure) and include some simulations studies.

Suggested Citation

  • Llop, P. & Forzani, L. & Fraiman, R., 2011. "On local times, density estimation and supervised classification from functional data," Journal of Multivariate Analysis, Elsevier, vol. 102(1), pages 73-86, January.
    • Handle: RePEc:eee:jmvana:v:102:y:2011:i:1:p:73-86
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    References listed on IDEAS

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    1. Castellana, J. V. & Leadbetter, M. R., 1986. "On smoothed probability density estimation for stationary processes," Stochastic Processes and their Applications, Elsevier, vol. 21(2), pages 179-193, February.
    2. Ferraty, F., 2010. "High-dimensional data: a fascinating statistical challenge," Journal of Multivariate Analysis, Elsevier, vol. 101(2), pages 305-306, February.
    3. Manteiga, Wenceslao Gonzalez & Vieu, Philippe, 2007. "Statistics for Functional Data," Computational Statistics & Data Analysis, Elsevier, vol. 51(10), pages 4788-4792, June.
    4. Blanke, D. & Bosq, D., 1997. "Accurate rates of density estimators for continuous-time processes," Statistics & Probability Letters, Elsevier, vol. 33(2), pages 185-191, April.
    5. Ferraty, F. & Vieu, P., 2003. "Curves discrimination: a nonparametric functional approach," Computational Statistics & Data Analysis, Elsevier, vol. 44(1-2), pages 161-173, October.
    6. Cuevas, Antonio & Fraiman, Ricardo, 2009. "On depth measures and dual statistics. A methodology for dealing with general data," Journal of Multivariate Analysis, Elsevier, vol. 100(4), pages 753-766, April.
    7. Labrador, Boris, 2008. "Strong pointwise consistency of the kT -occupation time density estimator," Statistics & Probability Letters, Elsevier, vol. 78(9), pages 1128-1137, July.
    8. Antonio Cuevas & Manuel Febrero & Ricardo Fraiman, 2007. "Robust estimation and classification for functional data via projection-based depth notions," Computational Statistics, Springer, vol. 22(3), pages 481-496, September.
    9. Cristian Preda & Gilbert Saporta & Caroline Lévéder, 2007. "PLS classification of functional data," Computational Statistics, Springer, vol. 22(2), pages 223-235, July.
    10. Gareth M. James & Trevor J. Hastie, 2001. "Functional linear discriminant analysis for irregularly sampled curves," Journal of the Royal Statistical Society Series B, Royal Statistical Society, vol. 63(3), pages 533-550.
    11. Boente, Graciela & Fraiman, Ricardo, 1988. "Consistency of a nonparametric estimate of a density function for dependent variables," Journal of Multivariate Analysis, Elsevier, vol. 25(1), pages 90-99, April.
    12. Li, Bin & Yu, Qingzhao, 2008. "Classification of functional data: A segmentation approach," Computational Statistics & Data Analysis, Elsevier, vol. 52(10), pages 4790-4800, June.
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    Cited by:

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