Nonparametric Density Estimation from Biased Data with Unknown Biasing Function
提出一种核密度估计方法，用于在抽样概率依赖于变量且偏倚函数未知时估计变量密度，需要两个独立样本，并给出渐近性质与实例验证。
Abstract 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 methodology is illustrated both on simulation data and on a dual-list dataset of aboriginal people in the Vancouver-Richmond area of Canada.