The effects of kernel choices in density estimation with biased data

This paper considers the effects of kernel choices on the large sample behaviors of a class of kernel estimates of the underlying density function f(x) when s independent selection biased samples are observed. Under the popular twice differentiable assumption on f, the main results show that, contrary to the well-known results in i.i.d. direct samples, the choices of kernels are important and the optimal kernels may be asymmetric and discontinuous when the weight functions of the biased samples have jumps.