Asymptotic distribution of data‐driven smoothers in density and regression estimation under dependence
- 18 December 1995
- journal article
- Published by Wiley in The Canadian Journal of Statistics / La Revue Canadienne de Statistique
- Vol. 23 (4) , 383-397
- https://doi.org/10.2307/3315382
Abstract
We consider automatic data‐driven density, regression and autoregression estimates, based on any random bandwidth selector h/T. We show that in a first‐order asymptotic approximation they behave as well as the related estimates obtained with the “optimal” bandwidthhTas long ashT/hT→ 1 in probability. The results are obtained for dependent observations; some of them are also new for independent observations.Keywords
This publication has 46 references indexed in Scilit:
- Properties of uniform consistency of the kernel estimators of density and regression functions under dependence assumptionsStochastics and Stochastic Reports, 1992
- Comparison of Two Bandwidth Selectors with Dependent ErrorsThe Annals of Statistics, 1991
- Data-Driven Smoothing Based on Convexity PropertiesPublished by Springer Nature ,1991
- Asymptotic Distribution of Robust Estimators for Nonparametric Models from Mixing ProcessesThe Annals of Statistics, 1990
- Jfon parametric time series analysis and prediction: uniform almost sure convergence of the window and jt-nn autoregression estimatesStatistics, 1985
- An alternative method of cross-validation for the smoothing of density estimatesBiometrika, 1984
- Asymptotic normality of some kernel-type estimators of probability densityStatistics & Probability Letters, 1983
- How Many Variables Should Be Entered in a Regression Equation?Journal of the American Statistical Association, 1983
- On Bandwidth Variation in Kernel Estimates-A Square Root LawThe Annals of Statistics, 1982
- On the Choice of Smoothing Parameters for Parzen Estimators of Probability Density FunctionsIEEE Transactions on Computers, 1976