Nonparametric Density Estimation from Biased Data with Unknown Biasing Function
偏倚函数未知时基于有偏样本的非参数密度估计
We present a kernel estimator for the density of a variable when sampling probabilities depend on that variable. Both the density and sampling bias weight functions are unknown and are estimated nonparametrically. To achieve this, the method requires that two independent samples be taken from a fixed finite population. An estimator of population size follows simply from our density estimator. Asymptotic bias and standard errors for these estimators are provided, and the…