Sequential estimation for the multiple linear regression models with balanced loss functions

Abstract

Sequential analysis (SA) as a sampling technique has notable advantages like smaller average sample size and reduced value of risk compared to similarly comparable fixed-sample techniques. In this study, we first propose a few models for the estimation of the regression parameters or functions of parameters under the multiple linear regression (MLR) setup using a balanced loss function (BLF). Thereafter, we obtain the expressions of risk functions and optimal fixed sample sizes for the proposed models based on the bounded risk criteria. We establish that no fixed-sample procedures can tackle these estimation problems. Hence, we propose different multistage sampling methodologies, viz. (i) two-stage sampling, (ii) three-stage sampling, (iii) purely sequential sampling, and (iv) batch sequential sampling, and corroborate the same with the detailed simulation and real data analyses.

Keywords:

• Advertising data
• balanced loss function
• bounded risk
• estimation
• LINEX loss
• multiple linear regression
• sequential sampling
• squared error loss
• stopping criteria

SUBJECT CLASSIFICATIONS:

• 62F10
• 62J05
• 62L12
• 62L15
• 62P25

ACKNOWLEDGMENTS

We thank the Editor-in-Chief Professor Nitis Mukhopadhyay, an Associate Editor, and three anonymous reviewers for critically evaluating the original manuscript. Their comments and suggestions led to this revised and significantly improved version.

DISCLOSURE

The authors have no conflict of interests to declare.