Estimation Of Models For Use In Model-based Statistical Sampling In Designs For Inventories.

Abstract

Model-based statistical sampling (MBSS) has been introduced as a promising method for constructing stratified sample designs used in the estimation of the total cost of an inventory. The MBSS methodology uses a linear model with heteroscedastic errors to construct strata. The model parameters used in MBSS are generally unknown and must be estimated. A maximum likelihood estimation (MLE) procedure assuming normally distributed residuals has been used in the past to estimate the model. However, the data in inventories are non-normal, and the MLE approach is sensitive to deviations from the normal distribution. The effects of inventory data on the MLE procedure's estimates and the subsequent effects on the MBSS sample designs are studied. A robust estimation (RRE) procedure, which should be less sensitive to deviations from the normal distribution, is developed as an alternative estimation procedure. The effects of inventory data on the RRE procedure's estimates and the subsequent effects on the MBSS sample designs are studied as well. Conventional statistical sampling, MBSS, characteristics of inventory data, empirical support for the model, and the derivations of the MLE and RRE procedures are examined. The effects of inventory data on the estimation procedures are observed through simulations using actual and generated inventory data. The simulation results are used to determine the subsequent effects of the estimation procedures on the MBSS sample designs. Results indicate that the MLE procedure is sensitive, while the RRE procedure is less sensitive to the deviations from the normal distribution found in inventory data. Also, model estimation for low error rate inventory populations can be improved. In some instances, blind use of the MLE or the RRE procedures yielded ineffective sample designs. However, prudent use of the MLE and RRE procedures along with adequate model evaluation should produce effective MBSS designs.