Use of asymmetric loss functions in sequential estimation problems for multiple linear regression

Abstract

When estimating in a practical situation, asymmetric loss functions are preferred over squared error loss functions, as the former is more appropriate than the latter in many estimation problems. We consider here the problem of fixed precision point estimation of a linear parametric function in beta for the multiple linear regression model using asymmetric loss functions. Due to the presence of nuissance parameters, the sample size for the estimation problem is not known beforehand and hence we take the recourse of adaptive multistage sampling methodologies. We discuss here some multistage sampling techniques and compare the performances of these methodologies using simulation runs. The implementation of the codes for our proposed models is accomplished utilizing MATLAB 7.0.1 program run on a Pentium IV machine. Finally, we highlight the significance of such asymmetric loss functions with few practical examples.

Keywords:

• loss function
• risk
• bounded risk
• asymmetric loss function
• LINEX loss function
• relative LINEX loss function
• stopping rule
• multistage sampling procedure
• purely sequential sampling procedure
• batch sequential sampling procedure

Acknowledgements

This research is part of the author's doctoral dissertation work at the Indian Institute of Management Calcutta, India. The author would like to acknowledge the financial grants made possible under project INS/IITK/IME/20040220.