Bias/Variance Trade-Off in Estimates of a Process Parameter Based on Temporal Data

Abstract

We recommend an approach to estimate a process performance measure (or parameter) at the present time from a stream of data where the performance may drift slowly over time. It is common practice to estimate current process performance using either present-time data only or including all historical data. When sample sizes by time period are small, an estimate based only on present-time data is imprecise. When the performance changes over time, including historical data in estimation trades more bias for less variability. We propose to regulate the bias/variance trade-off using estimating equations that down-weight past data. We derive approximations for the variance of the estimator and the distribution of a test statistic involving the estimator. The work is motivated by estimation of a customer loyalty measure where realistic data demonstrates the proposed approach.

• Net Promoter Score (NPS)
• Process Monitoring
• Weighted Estimating Equations

Additional information

Notes on contributors

Patricia L. Cooper Barfoot

Dr. Cooper Barfoot is a new graduate from the Department of Statistics and Actuarial Science. Her email address is [email protected].

Stefan H. Steiner

Dr. Steiner is Chair and Professor in the Department of Statistics and Actuarial Science. He is a Fellow of ASQ. His email address is [email protected].

R. Jock MacKay

Dr. MacKay is Professor Emeritus in the Department of Statistic and Actuarial Science. His email address is [email protected].