HETEROSCEDASTICITY IN SURVEY DATA AND MODEL SELECTION BASED ON WEIGHTED HANNAN-QUINN INFORMATION CRITERION
Keywords:
Hannan-Quinn Information Criterion, Weighted Hannan-Quinn Information Criterion, Differential Entropy, Log-Quantiles, Variance To Mean Ratio.Abstract
This paper made an attempt on the weighted version of Hannan-Quinn information criterion for the purpose of selecting a best model from various competing models, when heteroscedasticity is present in the survey data. The authors found that the information loss between the true model and fitted models are equally weighted, instead of giving unequal weights. The computation of weights purely depends on the differential entropy of each sample observation and traditional Hannan-Quinn information criterion was penalized by the weight function which comprised of the Inverse variance to mean ratio (VMR) of the fitted log quantiles.The Weighted Hannan-Quinn information criterion was explained in two versions based on the nature of the estimated error variances of the model namely Homogeneous and Heterogeneous WHQIC respectively. The WHQIC visualizes a transition in model selection and it leads to conduct a logical statistical treatment for selecting a best model. Finally, this procedure was numerically illustrated by fitting 12 different types of stepwise regression models based on 44 independent variables in a BSQ (Bank service Quality) study.
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