TITLE:
Likelihood Methods for Basic Stratified Sampling, with Application to Von Bertalanffy Growth Model Estimation
AUTHORS:
Nan Zheng, Noel Cadigan
KEYWORDS:
Length-Stratified Age Sampling, Response-Selective Sampling, Basic Stratified Sampling, Complete-Data Likelihood, Empirical Proportion Likelihood
JOURNAL NAME:
Open Journal of Statistics,
Vol.9 No.6,
November
26,
2019
ABSTRACT: This paper mainly addresses maximum likelihood
estimation for a response-selective stratified sampling scheme, the basic
stratified sampling (BSS), in which the maximum subsample size in each stratum
is fixed. We derived the complete-data likelihood for BSS, and extended it as a
full-data likelihood by incorporating incomplete data. We also similarly
extended the empirical proportion likelihood approach for consistent and
efficient estimation. We conducted a simulation study to compare these two new
approaches with the existing estimation methods in BSS. Our result indicates
that they perform as well as the standard full information likelihood approach.
Methods were illustrated using a growth model for fish size at age, including
between-individual variability. One of our major conclusions is that the fully
observed BSS data, the partially observed data used for stratification, and the
sampling strategy are all important in constructing a consistent and efficient
estimator.