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Weighted Split Sample Bootstrap for Regression Models with High Dimensional Data

Affiliations

  • Centre of Statistical and Decision Science Studies, Faculty of Computer and Mathematical Sciences, Universiti Teknologi MARA (UiTM) Shah Alam, Selangor, Malaysia

Abstract


Bootstrapping is a statistical resampling technique that can be used in the estimation of statistical measures. This computer-based method has great application in many statistical areas, including regression analysis. Numerous bootstrap methods have been introduced in regression analysis; but, methods that deliberately addressing regression models for high dimensional data are scarcely found. Many classical bootstrap methods cannot provide good estimates when outliers are present in data set. Hence, this study introduces a robust bootstrap method that is specially designed for regression models with high dimensional data (i.e., Partial Least Squares (PLS) regression). This proposed method is called Weighted Split Sample Bootstrap (WSSB). Its performance was compared to the Split Sample Bootstrap (SSB) method by means of standard errors, biases and confidence intervals of parameter estimates through simulation studies. Results indicate that WSSB outperforms SSB.

Keywords

Bootstrap, High Dimensional Data, Outliers, Partial Least Squares.

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