In this paper we derive rates of uniform strong convergence for the kernel estimator of the regression function in a left-truncation model. It is assumed that the lifetime observations with multivariate covariates form a stationary α-mixing sequence. The estimation of the covariate's density is considered as well. Under the assumption that the lifetime observations are bounded, we show that, by an appropriate choice of the bandwidth, both estimators of the covariate's density and regression function attain the optimal strong convergence rate known from independent complete samples.
Bibliographical noteFunding Information:
The authors would like to thank an associate editor and a referee for their careful reading of this manuscript and their helpful comments. This research was supported by the National Natural Science Foundation of China (10571136, 10871146), a grant from the Natural Sciences and Engineering Research Council of Canada, and the NSF grant DMS 0604176.
- Nonparametric regression estimator
- Strong convergence
- Truncated data
- α-mixing sequence