Measuring the Effect of Length-Biased Sampling When the Variable Being Sampled Is Unobserved

• Activity Number: 70
• Type: Invited
• Date/Time: Monday, August 4, 2003 : 8:30 AM to 10:20 AM
• Sponsor: Section on Physical and Engineering Sciences
• Author(s): Karen Kafadar*+
• Companies: University of Colorado, Denver
• Keywords: screening models ; length bias ; computer simulations ; exploratory analysis

Abstract

Length-biased sampling arises when items are sampled in proportion to their values on a random variable of interest. For example, older units may be more likely to be sampled simply because they have been in service for a longer period of time. The effect of this sampling bias on the estimate of the true population mean is well known when this random variable, say X, is observable. A more difficult situation arises when X is not observed, but the outcome of another random variable, say Y, is observed and is known to be correlated with X. This context may arise in an inspection program, wherein units with longer degradation phases are more likely to surface during a periodic routine inspection than units with shorter degradation phases. The mean lifetime of all units is then a function of the mean of the length-biased sampled units and the correlation between X and Y. However, to obtain practical answers, models must be developed. The implications of errors in these models will be discussed. We discuss theoretical as well as practical aspects of estimation of the true population mean in such situations.