Robust variable selection in linear regression models / Shokrya Saleha A. Alshqaq

Shokrya Saleha, A. Alshqaq (2015) Robust variable selection in linear regression models / Shokrya Saleha A. Alshqaq. PhD thesis, Universiti Malaya.

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Abstract

This study looks at two problems related to the robust variable selection in linear regression models with six objectives in mind. The first three objectives are concerned with the problem of selection variables in small data sets in a linear regression model. The first is the investigation of the robustness of various best variable selection criteria in the presence of outliers and leverage points in the data set. The second derives the influence function of AIC, Cp, and SIC criteria and discussed the properties of these functions. The third is to explore the role of two robust methods for selecting the best variable in the linear regression. The first approach considered is a modified version of AIC, Cp, and SIC statistics by utilizing the high breakdown point estimators of the regression model. The other methods are based on diagnostic regression approach using outliers and leverage diagnostics in regression model procedures. For each method, the power of performance is compared with classical non-robust criteria and the existing criteria, based on M-estimation. In general, our findings show that these criteria are capable of selecting the appropriate models in the presence of outliers. The following three objectives look at the development of LASSO variable selection regression to solve the problem of multicollinearity and large data in variable selection procedure. The fourth is to investigate the sensitivity of non-robust LASSO (LASSO and adaptive-LASSO) and robust LASSO (LAD-LASSO and Huber-LASSO) toward the existence of outliers and leverage points in the data. The fifth looks at extending the Huber-LASSO to include more robust estimators. We present the GM-LASSO and MM-LASSO methods. If the multicollinearity does exist, we use the idea of the LASSO regression analysis to find the best variable in the model. The performance of these methods has also been compared with classical non-robust LASSO, and the existing robust LAD-LASSO and Huber-LASSO are generally good. The final objective is to prepare a new LASSO method based on diagnostic regression approach.

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