Groupe d’études et de recherche en analyse des décisions

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

Raghu Nandan Sengupta Indian Institute of Technology Kanpur, Inde

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.

Publication: Journal of Applied Statistics, 2008, 35, 3, 245-261.