Variance Function Estimation using Signal-to-Noise Ratio

By : Soham Chakraborty , Pathik Mandal

Page No: 178-211

Abstract
A new methodology is developed for estimating the variance function in a heteroscedastic regression set up with a focus on small sample regression based estimation. The three main features of the proposed methodology are as follows: (i) Signal-to-noise ratio is used as the response for the purpose of regression instead of a function of only the residuals of the fitted mean function, (ii) Before fitting the variance function, the data are trimmed following an optimal trimming procedure and (iii) The estimates of the parameters of the variance function obtained from the trimmed data are adjusted to minimize the mean square error of the estimates of variances. The effectiveness of the proposed methods of trimming and adjustments are demonstrated through extensive simulation. It is shown that the variances can be estimated more accurately as above compared to those obtained directly from an estimate of the corresponding variance function. Four sets of real life data are also analyzed for the purpose of illustration.

Authors :
Soham Chakraborty
SQC & OR Unit, Indian Statistical Institute, Kolkata.

Pathik Mandal
SQC & OR Unit, Indian Statistical Institute, Kolkata.

DOI: DOI-https://doi.org/10.32381/IAPQRT.2019.43.02.5