A confidence interval for the median of a finite population under unequal probability sampling: A model-assisted approach

This paper presents a method for constructing confidence intervals for the median of a finite population under unequal probability sampling. The model-assisted approach makes use of the _L1$L_1$-norm to motivate the estimating function which is then used to develop a unified approach to inference which includes not only confidence intervals but hypothesis tests and point estimates. The approach relies on large sample theory to construct the confidence intervals. In cases when second-order inclusion probabilities are not available or easy to compute, the Hartley–Rao variance approximation is employed. Simulations show that the confidence intervals achieve the appropriate confidence level, whether or not the Hartley–Rao variance is employed.     

Confidence Intervals for the Median of a Finite Population Based on the Sign Test

This article presents methods for constructing confidence intervals for the median of a finite population under simple random sampling without replacement, stratified random sampling, and cluster sampling. The confidence intervals, as well as point estimates and test statistics, are derived from sign estimating functions which are based on the well-known sign test. Therefore, a unified approach for inference about the median of a finite population is given.     

KERNEL DENSITY ESTIMATION WITH MISSING DATA AND AUXILIARY VARIABLES

In most parametric statistical analyses, knowledge of the distribution of the response variable, or of the errors, is important. As this distribution is not typically known with certainty, one might initially construct a histogram or estimate the density of the variable of interest to gain insight regarding the distribution and its characteristics. However, when the response variable is incomplete, a histogram will only provide a representation of the distribution of the observed data. In the AIDS Clinical Trial Study protocol 175, interest lies in the difference in CD4 counts from baseline to final follow-up, but CD4 counts collected at final follow-up were incomplete. A method is therefore proposed for estimating the density of an incomplete response variable when auxiliary data are available. The proposed estimator is based on the Horvitz–Thompson estimator, and the propensity scores are estimated nonparametrically. Simulation studies indicate that the proposed estimator performs well.