I am interested in non-parametric methods for building confidence intervals for an estimator (e.g. the mean) using few samples (e.g. 10). I think I have read somewhere that smoothing the bootstrapped estimator values can improve the quality of the derived percentiles interval. However I could not find any online reference that explains how to tune the bandwidth of the smoothing step.
Sorry to be answering so late. This question came just when I joined CV and i only found it by looking back. For your specific question about using the bootstrap in kernel density estimation I think you will find material in Bernard Silverman's book. I think he covers the use of bootstrap for bandwidth selection.
Efron and Tibshirani discuss the bootstrap for finding modes of a density via kernel methods.
Oddly there is not really much on it in the general text on bootstrap including mine. Maybe in the next edition I will add something.
Bootstrap confidence intervals
Thomas J. DiCiccio and Bradley Efron Source: Statist. Sci. Volume 11, Number 3 (1996), 189-228.
Keywords: Bootstrap-t; BCa and ABC methods; calibration; second-order accuracy