nonparametric regression; right censoring; Kernel estimation
Abstract :
[en] In this paper, we study strong uniform consistency of a weighted average of artificial data points. This is especially useful when information is incomplete (censored data, missing data ...). In this case, reconstruction of the information is often achieved nonparametrically by using a local preservation of mean criterion for which the corresponding mean is estimated by a weighted average of new data points. The present approach enlarges the possible scope for applications beyond just the incomplete data context and can also be useful to treat the estimation of the conditional mean of specific functions of complete data points. As a consequence, we establish the strong uniform consistency of the Nadaraya - Watson [Nadaraya, E.A., 1964. On estimating regression. Theory Probab. Appl. 9, 141 - 142; Watson, G.S., 1964. Smooth regression analysis. Sankhya Ser. A 26, 359 - 372] estimator for general transformations of the data points. This result generalizes the one of Hardle et al. [Strong uniform consistency rates for estimators of conditional functionals. Ann. Statist. 16, 1428 - 1449]. In addition, the strong uniform consistency of a modulus of continuity will be obtained for this estimator. Applications of those two results are detailed for some popular estimators. (c) 2007 Elsevier B.V. All rights reserved.
Disciplines :
Mathematics
Author, co-author :
Heuchenne, Cédric ; Université de Liège - ULiège > HEC - École de gestion de l'ULiège > Statistique appliquée à la gestion et à l'économie
Language :
English
Title :
Strong uniform consistency results of the weighted average of conditional artificial data points
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Bibliography
Beran, R., 1981. Nonparametric regression with randomly censored survival data. Technical Report, University of California, Berkeley.
Buckley J., and James I.R. Linear regression with censored data. Biometrika 66 (1979) 429-436
Cheng P.E. Nonparametric estimation of mean functionals with data missing at random. J. Amer. Statist. Assoc. 89 (1994) 81-87
Cheng P.E., and Chu C.K. Kernel estimation of distribution functions and quantiles with missing data. Statist. Sinica 6 (1996) 63-78
Chu C.K., and Cheng P.E. Nonparametric regression estimation with missing data. J. Statist. Plann. Infererence 48 (1995) 85-99
Fan J., and Gijbels I. Censored regression: local linear approximations and their applications. J. Amer. Statist. Assoc. 89 (1994) 560-570
Härdle W., Janssen P., and Serfling R. Strong uniform consistency rates for estimators of conditional functionals. Ann. Statist. 16 (1988) 1428-1449
Heuchenne, C., Van Keilegom, I., 2004. Polynomial regression with censored data based on preliminary nonparametric estimation. Ann. Inst. Statist. Math. 59, 273-298.
Heuchenne, C., Van Keilegom, I., 2005. Mean preservation in nonparametric regression with censored data. J. Multivariate Anal. (to appear).
Koul H., Susarla V., and Van Ryzin J. Regression analysis with randomly right-censored data. Ann. Statist. 9 (1981) 1276-1288
Leurgans S. Linear models, random censoring and synthetic data. Biometrika 74 (1987) 301-309
Little R.J.A., and Rubin D.B. Statistical Analysis with Missing Data (1987), Wiley, New York
Masry E. Multivariate local polynomial regression for time series: uniform strong consistency and rates. J. Time Ser. Anal. 17 (1996) 571-599
Nadaraya E.A. On estimating regression. Theory Probab. Appl. 9 (1964) 141-142
Stone C.J. Consistent nonparametric regression. Ann. Statist. 5 (1977) 595-645
Van Keilegom I., and Akritas M.G. Transfer of tail information in censored regression models. Ann. Statist. 27 (1999) 1745-1784
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