Asymmetric Penalized Prediction Using Adaptive Sampling Procedures

Abstract

Prediction using a multiple-regression model is addressed when the penalties for overpredicting and underpredicting the true future value are not equal. Such asymmetric penalty functions are appropriate in many practical situations. If one imposes some preassigned precision on the prediction procedure, it is shown that in the presence of nuisance parameters in the model, the sample size needed to achieve the fixed precision is unknown. Some adaptive multistage sampling techniques are discussed that offer solutions to this problem. A prediction procedure based on a purely sequential sampling scheme is introduced, followed by a batch sequential scheme. Finally, a real-life example is provided to illustrate the use of these procedures, and computational evidence is supplied to demonstrate the efficiency of the latter procedure compared to the former one.

Key Words:

• Accelerated sequential sampling
• Bounded risk forecasting
• LINEX loss function
• Multistage
• Purely sequential
• Two-stage

Subject classification:

• 62L12
• 62J05

ACKNOWLEDGMENTS

The work of the first author is supported in part by a grant from the Indian Institute of Management Calcutta. The authors would like to thank an associate editor and two anonymous reviewers for several helpful comments.

Notes

Recommended by Madhuri Mulekar