On Kernel Smoothing and Horvitz-Thompson Estimation

Estimation of the total value of fixed characteristic of interest in a finite population is considered for a complex sampling scheme featuring unknown inclusion probabilities. The general empirical Horvitz-Thompson statistic is adopted as an estimator for the unknown total. In the presence of additional knowledge on inclusion probabilities taking form of inequality constraints it is proposed to use the well-known kernel estimator for individual inclusion probabilities. For a fixed-cost sequential sampling scheme this leads to a new nonparametric empirical Horvitz-Thompson estimator of a total. Its properties are compared to known alternatives in a simulation study.