  The Horvitz-Thompson (HT) estimator is widely used in survey sampling.
However, the variance of the HT estimator becomes large when the inclusion
probabilities are highly heterogeneous. To overcome this shortcoming, in this
paper, a hard-threshold method is used for the first-order inclusion
probabilities, that is, we carefully choose a threshold value, then replace the
inclusion probabilities smaller than the threshold by the threshold. By this
shrinkage strategy, we propose a new estimator called improved Horvitz-Thompson
(IHT) estimator to estimate the population total. The IHT estimator increases
the estimation accuracy although it brings bias which is relatively small. We
derive the IHT estimator's MSE and its unbiased estimator, and theoretically
compare the IHT estimator with the HT estimator. We also apply our idea to
construct the improved ratio estimator. We numerically analyze simulated and
real data sets to illustrate that the proposed estimators are more efficient
and robust than the classical estimators.
