Quantile Processes and their Applications in Finite Populations

Music City Center 

In this talk, I shall discuss the weak convergence of the quantile processes, which are constructed based on different estimators of the finite population quantiles under various well-known sampling designs. The results related to the weak convergence of these quantile processes are applied to find asymptotic distributions of the smooth L-estimators and the estimators of smooth functions of finite population quantiles. Based on these asymptotic distributions, confidence intervals are constructed for several finite population parameters like the median, the α-trimmed means, the interquartile range and the quantile based measure of skewness.

High entropy sampling designs

Ratio estimator

Regression estimator

Stratified multistage cluster sampling designs

Skorohod metric

Hadamard differentiability