  We are interested in renewable estimations and algorithms for nonparametric
models with streaming data. In our method, the nonparametric function of
interest is expressed through a functional depending on a weight function and a
conditional distribution function (CDF). The CDF is estimated by renewable
kernel estimations combined with function interpolations, based on which we
propose the method of renewable weighted composite quantile regression (WCQR).
Then we fully use the model structure and obtain new selectors for the weight
function, such that the WCQR can achieve asymptotic unbiasness when estimating
specific functions in the model. We also propose practical bandwidth selectors
for streaming data and find the optimal weight function minimizing the
asymptotic variance. The asymptotical results show that our estimator is almost
equivalent to the oracle estimator obtained from the entire data together.
Besides, our method also enjoys adaptiveness to error distributions, robustness
to outliers, and efficiency in both estimation and computation. Simulation
studies and real data analyses further confirm our theoretical findings.

Computation;Methodology