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High-Dimensional Nonlinear Optimization Problem in Semiparametric Regression Model

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Innovations in Multivariate Statistical Modeling

Part of the book series: Emerging Topics in Statistics and Biostatistics ((ETSB))

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Abstract

By evolving science, knowledge, and technology, new and precise methods for measuring, collecting, and recording information have been innovated, which have been resulted in the appearance and developing of high-dimensional data, in which the number of explanatory variables is much larger than the number of observations. Analysis and modeling the high-dimensional data is one of the most challenging problems faced by the world today. Interpreting such data is not easy and needs to use the modern methods. Penalized methods are one of the most popular ways to analyze the high-dimensional data. Semiparametric models, which a combination of both parametric and nonparametric models, are very flexible models. They are useful when the model contains both parametric and nonparametric elements in the data set. As known, the LASSO approach is a popular technique for variable selection in high-dimensional sparse regression models. Here, we show that the prediction performance of the LASSO method can be improved by eliminating the structured noises. The main purpose of this research is to introduce a modified variable selection or estimation method for a high-dimensional semiparametric regression model through a nonlinear mixed-integer programming technique. Finally, the performance of the proposed method is examined through a real-data analysis about the production of vitamin B2 and some Monte-Carlo simulation studies.

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Acknowledgements

The author thank the anonymous Reviewers and the Associate Editor for their valuable comments and suggestions that helped to improve the quality of this work.

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Authors and Affiliations

  1. Department of Statistics, Faculty of Mathematics, Statistics and Computer Sciences, Semnan University, P.O. Box 35195-363, Semnan, Iran

    Mahdi Roozbeh

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  1. Mahdi Roozbeh
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Correspondence to Mahdi Roozbeh .

Editor information

Editors and Affiliations

  1. Department of Statistics, University of Pretoria, Pretoria, South Africa

    Andriëtte Bekker

  2. Department of Statistics, University of Pretoria, Pretoria, South Africa

    Johannes T. Ferreira

  3. Department of Statistics, Ferdowsi University of Mashhad, Mashhad, Iran

    Mohammad Arashi

  4. Department of Statistics, University of Pretoria, Pretoria, South Africa

    Ding-Geng Chen

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Roozbeh, M. (2022). High-Dimensional Nonlinear Optimization Problem in Semiparametric Regression Model. In: Bekker, A., Ferreira, J.T., Arashi, M., Chen, DG. (eds) Innovations in Multivariate Statistical Modeling. Emerging Topics in Statistics and Biostatistics . Springer, Cham. https://doi.org/10.1007/978-3-031-13971-0_16

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