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Two-Stage Nonparametric Regression for Longitudinal Data

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  • Rodríguez Poo, Juan M.
  • Núñez Antón, Vicente Alfredo
  • Ferreira García, María Eva

Abstract

In the analysis of longitudinal data it is of main interest to investigate the existence of group and individual effects under correlated observations across time. In this paper, we develop a nonparametric two-step procedure that enables us to estimate group effects under a very general form of correlation across time. Moreover, we propose several methods to estimate the bandwidth and show their asymptotyc optimality. Since the asymptotic distribution is untractable, we develop a randomization test that is suitable for testing the group effects. Finally, we apply the estimation procedure, the bandwidth selection criteria and the randomization test to the data from the Iowa Cochlear Implant Project.

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Paper provided by Universidad del País Vasco - Departamento de Economía Aplicada III (Econometría y Estadística) in its series BILTOKI with number 1999-01.

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Date of creation: Jan 1999
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Handle: RePEc:ehu:biltok:199901

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Postal: Dpto. de Econometría y Estadística, Facultad de CC. Económicas y Empresariales, Universidad del País Vasco, Avda. Lehendakari Aguirre 83, 48015 Bilbao, Spain
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Keywords: Kernel estimation; bandwidth selection; nonstationary errors; group effects; randomization test;

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  1. Ferreira, Eva & Núñez-Antón, Vicente & Rodríguez-Póo, Juan, 1997. "Kernel regression estimates of growth curves using nonstationary correlated errors," Statistics & Probability Letters, Elsevier, vol. 34(4), pages 413-423, June.
  2. Fraiman, R. & Meloche, J., 1994. "Smoothing dependent observations," Statistics & Probability Letters, Elsevier, vol. 21(3), pages 203-214, October.
  3. Marron, James Stephen & Härdle, Wolfgang, 1986. "Random approximations to some measures of accuracy in nonparametric curve estimation," Journal of Multivariate Analysis, Elsevier, vol. 20(1), pages 91-113, October.
  4. Hart, Jeffrey D. & Wehrly, Thomas E., 1993. "Consistency of cross-validation when the data are curves," Stochastic Processes and their Applications, Elsevier, vol. 45(2), pages 351-361, April.
  5. Vicente Núñez-Antón & Juan Rodríguez-Póo & Philippe Vieu, 1999. "Longitudinal data with nonstationary errors: a nonparametric three-stage approach," TEST: An Official Journal of the Spanish Society of Statistics and Operations Research, Springer, vol. 8(1), pages 201-231, June.
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