Local linear estimation of conditional cumulative distribution function in the functional data: Uniform consistency with convergence rates
Chaima Hebchi; Abdelhak Chouaf
Kybernetika (2021)
- Volume: 57, Issue: 5, page 819-839
- ISSN: 0023-5954
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topHebchi, Chaima, and Chouaf, Abdelhak. "Local linear estimation of conditional cumulative distribution function in the functional data: Uniform consistency with convergence rates." Kybernetika 57.5 (2021): 819-839. <http://eudml.org/doc/297572>.
@article{Hebchi2021,
abstract = {In this paper, we investigate the problem of the conditional cumulative of a scalar response variable given a random variable taking values in a semi-metric space. The uniform almost complete consistency of this estimate is stated under some conditions. Moreover, as an application, we use the obtained results to derive some asymptotic properties for the local linear estimator of the conditional quantile.},
author = {Hebchi, Chaima, Chouaf, Abdelhak},
journal = {Kybernetika},
keywords = {functional data; local linear estimator; conditional cumulative; conditional quantile; nonparametric regression; small balls probability},
language = {eng},
number = {5},
pages = {819-839},
publisher = {Institute of Information Theory and Automation AS CR},
title = {Local linear estimation of conditional cumulative distribution function in the functional data: Uniform consistency with convergence rates},
url = {http://eudml.org/doc/297572},
volume = {57},
year = {2021},
}
TY - JOUR
AU - Hebchi, Chaima
AU - Chouaf, Abdelhak
TI - Local linear estimation of conditional cumulative distribution function in the functional data: Uniform consistency with convergence rates
JO - Kybernetika
PY - 2021
PB - Institute of Information Theory and Automation AS CR
VL - 57
IS - 5
SP - 819
EP - 839
AB - In this paper, we investigate the problem of the conditional cumulative of a scalar response variable given a random variable taking values in a semi-metric space. The uniform almost complete consistency of this estimate is stated under some conditions. Moreover, as an application, we use the obtained results to derive some asymptotic properties for the local linear estimator of the conditional quantile.
LA - eng
KW - functional data; local linear estimator; conditional cumulative; conditional quantile; nonparametric regression; small balls probability
UR - http://eudml.org/doc/297572
ER -
References
top- Barrientos-Marin, J., Ferraty, F., Vieu, P., , J. Nonparametr. Statist. 22 (2010), 617-632. DOI
- Baillo, A., Grané, A., , Journal of Multivariate Analysis. 100 (2009), 102-111. DOI
- Berlinet, A., Gannoun, A., Matzner-Lober, E., , Canadian J. Statistics. 26 (1998), 365-380. DOI
- Fortiana, E. Boj P. Delicado J., , Computational Statistics and Data Analysis 54 (2010), 429-437. DOI
- Bosq, D., 10.1007/978-1-4612-1154-9_8, Lecture Notes in Statistics. 149 (2000), Springer-Verlag. DOI10.1007/978-1-4612-1154-9_8
- Bouanani, O., Laksaci, A., Rachdi, R., Rahmani, S., , Behaviormetrika 46 (2019), 199-233. DOI
- Demongeot, J., Laksaci, A., Madani, F., Rachdi, M., A fast functional locally modeled conditional density and mode for functional time-series., Recent Advances in Functional Data Analysis and Related Topics, Contributions to Statistics, Physica-Verlag/Springer 2011, pp. 85-90.
- Demongeot, J., Laksaci, A., Madani, F., Rachdi, M., , Statistics 47 (2013), 26-44. DOI
- J.Demongeot, Laksaci, A., Rachdi, M., Rahmani, S., , Sankhya A 76 (2014), 2, 328-355. DOI
- Fan, J., , J. Amer. Statist. Assoc. 87 (1992), 998-1004. DOI
- Fan, J., Gijbels, I., Local Polynomial Modelling and its Applications., Chapman and Hall, London 1996.
- Fan, J., Yao, Q., Nolinear Time Series : Nonparametric and Parametric Methods., (2003) Springer-Verlag, New York.
- Ferraty, F., Vieu, P., Nonparametric Functional Data Analysis. Theory and Practice., Springer Series in Statistics. New York 2006.
- Ferraty, F., Laksaci, A., Tadj, A., Vieu, P., , J. Statist. Plann. Inference 140 (2010), 335-352. DOI
- Gannoun, A., Saracco, J., Yu, K., , J. Statist. Plann. Inference 117 (2003), 207-223. DOI
- Honda, T., , Annals of the Institute of Statistical Mathematics 52 (2000), 459-470. DOI
- Kima, C., Ohb, M., Yangc, S., Choi, H., , J. Korean Statist. Soc. 39 (2010), 347-355. DOI
- Koenker, R., , J. Econometrics 95 (2000), 2, 347-374. DOI
- Koenker, R., Quantile Regression., Cambridge University Press, 2005. Zbl1236.62031
- Koul, H. L, Mukherjee, , Journal of Multivariate Analysis 51 (1994), 318-337. DOI
- Portnoy, S. L., , Journal of Multivariate Analysis 38 (1991), 100-113. DOI
- Rachdi, M., Laksaci, A., Demongeot, J., Abdali, A., Madani, F., , Comput.l Statist. and Data Anal. 73 (2014), 53-68. DOI
- Ramsay, J. O., Silverman, B. W., Functional Data Analysis Second edition., Springer, New York 2005.
- Roussas, G. G., , Bull. Soc. Math. Greece (N.S.) 9 (1968), 29-43. DOI
- Samanta, M., , Statistics and Probability Letters. vol. 7, issue 5 (1989), 407-412. DOI
- Stone, C. J., , Ann. Statist. 5 (1977), 595-645. DOI
- Stute, W., , Ann. Statist. 14(2) (1986), 638-647. DOI
- Tanner, M. A., Wong, W. H., , Ann. Statist. 11 (1983), 989-993. DOI
- Uspensky, J. V., Introduction to Mathematical Probability., McGraw-Hill Book Company 1937.
- Watson, G. S., Leadbetter, M. R., , Biometrika 51 (1964), 175-184. DOI
- Xiong, X., Zhou, P., Ailian, Ch., , Comm. Statist. Theory Methods 47 (2017), 3418-3440. DOI
- Youndjé, E., Sarda, P., Vieu, P., , Test 5 (1996), 379-394. DOI
- Yu, K., Lu, Z., Stander, J., , The Statistician 52 (2003), 331-350. DOI
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