ESTIMATION OF REGRESSION COEFFICIENTS USING GEOMETRIC MEAN OF SQUARED ERROR FOR SINGLE INDEX LINEAR REGRESSION MODEL
| Main Author: | Prasanna Mayilvahanan |
|---|---|
| Format: | Article |
| Terbitan: |
, 2018
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| Subjects: | |
| Online Access: |
https://zenodo.org/record/1252239 |
Daftar Isi:
- Regression models and their statistical analyses is one of the most important tool used by scientists and practitioners. The aim of a regression model is to fit parametric functions to data. It is known that the true regression is unknown and specific methods are created and used strictly pertaining to the problem. For the pioneering work to develop procedures for fitting functions, we refer to the work on the methods of least absolute deviations, least squares deviations and minimax absolute deviations. Today’s widely celebrated procedure of the method of least squares for function fitting is credited to the published works of Legendre and Gauss. However, the least squares based models in practice may fail to provide optimal results in non- Gaussian situations especially when the errors follow distributions with the fat tails. In this paper an unorthodox method of estimating linear regression coefficients by minimising GMSE(geometric mean of squared errors) is explored. Though GMSE(geometric mean of squared errors) is used to compare models it is rarely used to obtain the coefficients. Such a method is tedious to handle due to the large number of roots obtained by minimisation of the loss function. This paper offers a way to tackle that problem. Application is illustrated with the ‘Advertising’ dataset from ISLR and the obtained results are compared with the results of the method of least squares for single index linear regression model.