Improved Horvitz-Thompson Estimator in Survey Sampling

04/11/2018
by   Xianpeng Zong, et al.
0

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.

READ FULL TEXT
research
09/12/2019

Synthetic estimation for the complier average causal effect

We propose an improved estimator of the complier average causal effect (...
research
03/10/2021

A cautionary note on the Hanurav-Vijayan sampling algorithm

We consider the Hanurav-Vijayan sampling design, which is the default me...
research
12/02/2013

The Law of Total Odds

The law of total probability may be deployed in binary classification ex...
research
03/19/2019

Trimming and threshold selection in extremes

We consider removing lower order statistics from the classical Hill esti...
research
09/20/2016

Robust Estimation of Multiple Inlier Structures

The robust estimator presented in this paper processes each structure in...
research
10/29/2019

Spatial Spread Sampling Using Weakly Associated Vectors

Geographical data are generally autocorrelated. In this case, it is pref...
research
01/14/2021

Enhanced Cube Implementation For Highly Stratified Population

A balanced sampling design should always be the adopted strategies if au...

Please sign up or login with your details

Forgot password? Click here to reset