In this Note, we consider the problem of estimating the regression function for a fixed design model, when we only have access to quantized and correlated data. In order for the constructed estimate to be consistent, we assume that repeated observations are available. We give the asymptotic performance in terms of the mean squared error for the regression function estimator constructed from quantized observations, and we generate the optimal bandwidth.
Dans cette Note, nous considérons le problème d'estimation de la courbe de croissance pour des données quantifiées et corrélées. Afin que l'estimateur construit soit consistant, nous supposons disposer d'observations répetées. Nous donnons le comportement asymptotique de l'estimateur construit à partir de données quantifiées et nous déduisons la largeur de fenêtre optimale.
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@article{CRMATH_2005__340_12_901_0, author = {Benhenni, Karim and Rachdi, Mustapha}, title = {Non-parametric estimation of the average growth curve from quantized observations and correlated errors}, journal = {Comptes Rendus. Math\'ematique}, pages = {901--904}, publisher = {Elsevier}, volume = {340}, number = {12}, year = {2005}, doi = {10.1016/j.crma.2005.04.035}, language = {en}, url = {http://archive.numdam.org/articles/10.1016/j.crma.2005.04.035/} }
TY - JOUR AU - Benhenni, Karim AU - Rachdi, Mustapha TI - Non-parametric estimation of the average growth curve from quantized observations and correlated errors JO - Comptes Rendus. Mathématique PY - 2005 SP - 901 EP - 904 VL - 340 IS - 12 PB - Elsevier UR - http://archive.numdam.org/articles/10.1016/j.crma.2005.04.035/ DO - 10.1016/j.crma.2005.04.035 LA - en ID - CRMATH_2005__340_12_901_0 ER -
%0 Journal Article %A Benhenni, Karim %A Rachdi, Mustapha %T Non-parametric estimation of the average growth curve from quantized observations and correlated errors %J Comptes Rendus. Mathématique %D 2005 %P 901-904 %V 340 %N 12 %I Elsevier %U http://archive.numdam.org/articles/10.1016/j.crma.2005.04.035/ %R 10.1016/j.crma.2005.04.035 %G en %F CRMATH_2005__340_12_901_0
Benhenni, Karim; Rachdi, Mustapha. Non-parametric estimation of the average growth curve from quantized observations and correlated errors. Comptes Rendus. Mathématique, Volume 340 (2005) no. 12, pp. 901-904. doi : 10.1016/j.crma.2005.04.035. http://archive.numdam.org/articles/10.1016/j.crma.2005.04.035/
[1] The effect of quantization on the performance of sampling designs, IEEE Trans. Inform. Theory, Volume 44 (1998) no. 5, pp. 1981-1992
[2] A simple class of asymptotically optimal quantizers, IEEE Trans. Inform. Theory, Volume IT-29 (1983), pp. 666-676
[3] Estimating regression functions and their derivatives by the kernel method, Scand. J. Statist., Volume 11 (1984), pp. 171-185
[4] Quantization, IEEE Trans. Inform. Theory, Volume 44 (1998) no. 6, pp. 2325-2383
[5] , Applied Nonparametric Regression, vol. 19, Cambridge University Press, Cambridge, 1989
[6] Kernel regression estimation using repeated measurements data, J. Amer. Statist. Assoc., Volume 81 (1986), pp. 1080-1088
[7] Interval estimation of a normal process mean from rounded data, J. Qual. Technol., Volume 33 (2001), pp. 335-348
[8] Likelihood-based statistical estimation from quantized data, IEEE Trans. Instrum. Meas., Volume 54 (2005) no. 1, pp. 409-414
[9] Interval estimation of a normal process standard deviation from rounded data, Commun. Statist. Simulat., Volume 31 (2002), pp. 13-34
[10] Nonparametric function estimation for clustered data when the predictor is measured without/with error, J. Amer. Statist. Assoc., Volume 95 (2000) no. 450, pp. 520-534
[11] Minimum mean-square error quadrature, J. Statist. Comput. Simulat., Volume 46 (1993), pp. 217-234
[12] The growth curve model: a review, Commun. Statist. Theory Method, Volume 20 (1991) no. 9, pp. 2791-2822
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