Indian Journal of Science and Technology
Year: 2019, Volume: 12, Issue: 10, Pages: 1-7
Fazli Rabbi1*, Salahuddin2, Alamgir1 and Najma3
1Department of Statistics, University of Peshawar, Khyber Pakhtunkhwa, Pakistan;
2CECOS University of IT and Emerging Sciences, Hayatabad, Peshawar, Khyber Pakhtunkhwa, Pakistan; [email protected]
3Shaheed Benazir Bhutto Women University, Peshawar, Khyber Pakhtunkhwa, Pakistan;
*Author for correspondence
Department of Statistics, University of Peshawar, Khyber Pakhtunkhwa, Pakistan.
Email: [email protected]
Objectives: To develop a robust paired bootstrap criterion for linear model selection and to compare the performance of the proposed criterion across different error distributions. Methods/Analysis: Our proposed robust paired bootstrap criterion is based on a robust conditional expected prediction loss function. We estimate the robust conditional expected prediction loss by using the m-out-of-n stratified bootstrap approach. The m-out-of-n bootstrap procedure is considered to obtain the asymptotic consistency. The effects of large residuals are reduced by using a robust ρ function. Model with a minimum robust prediction loss is used as a selection criterion. The usefulness of our proposed robust model selection procedure is investigated through real data set and Monte Carlo simulations under a variety of contamination and error structures. Findings: The conventional least squares selection procedures generally fail in the existence of outliers or in heavy-tailed error distributions. The stratified bootstrap selection procedure has shown good results as compared to simple bootstrap procedure. The proposed robust method has shown good robustness features with contaminated normal and heavy-tailed distributions. The proposed criterion outperforms the alternative procedure in both situations, i.e. in contamination-free data as well as in contaminated data. Applications: The model selection procedure has a large number of applications including life sciences, social sciences, business or economics. The proposed criterion can be used in both cases, i.e. in contamination-free data as well as in contaminated data, to select a model.
Keywords: MM Estimation, Outliers, Stratified Bootstrap, Out-Of-Bag Bootstrap, Robust Expected Prediction Loss
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