HOW TO MODEL THE COMPLEX WORLD?
Xu Guo
School of Statistics, Beijing Normal University, Beijing, China.
Keywords: Parametric regression, Regression analysis and interpretability
Abstract

Regression analysis is a powerful tool to describe the relationship between response and predictors. In practice, parametric regression models such as linear regression models are widely used due to their simplicity and interpretability. When a parametric regression model is correctly fitted by the data, further statistical analysis can be easily and accurately elaborated with good explanations. However, such further analysis and interpretation could be misleading when the model does not fit the data well.

Article Information

Identifiers and Pagination:
Year:2016
Volume:1
First Page:3
Last Page:4
Publisher Id:.1:1.2016
Article History:
Received:December 13, 2016
Accepted:December 21, 2016
Collection year:2016
First Published:December 27, 2016

Regression analysis is a powerful tool to describe the relationship between response and predictors. In practice, parametric regression models such as linear regression models are widely used due to their simplicity and interpretability. When a parametric regression model is correctly fitted by the data, further statistical analysis can be easily and accurately elaborated with good explanations. However, such further analysis and interpretation could be misleading when the model does not fit the data well. A practical example is production theory in economics, in which the Cobb-Douglas function is commonly used to describe the linear relationship between the login puts, such as labor and capital, and the log-output. However, this function may not well describe the relationship. To avoid model mis-specification, nonparametric regression models are developed. The models are very °exifble, but loss some interpretability. Further, when the dimension of predictors is large, the estimation results obtained from nonparametric regression models can be very poor. This is documented as the curse of dimensionality. As a compromise, semi-parametric regression models are introduced. The models include partial linear regression model, single index model, additive model, varying coe±cient model, and so on. These semi-parametric regression models describe the relationship between the response and the predictors in a semi-parametric approach. That is, some features are specified in details and other parts are not. This makes the modeling process not only simple but also °exible enough.

The journal Advanced Calculation and Analysis welcomes contributions to all aspects of regression modeling, including model selection, model average, model checking, predicting, variable selection, semi/non-parametric regression models, regression models for missing, censored, functional and high-dimensional data. Advanced Calculation and Analysis is particularly interested in papers motivated by, and ¯t for, contemporary data analytic challenges. Methods should be validated through standard mathematical arguments that may be complemented with asymptotic arguments or computer-based experiments. Illustrations with relevant, original data are strongly encouraged when presented with clear contextual justification and explanation.


© 2016 The Author(s). This open access article is distributed under a Creative Commons Attribution (CC-BY) 4.0 license. You are free to: Share — copy and redistribute the material in any medium or format Adapt — remix, transform, and build upon the material for any purpose, even commercially. The licensor cannot revoke these freedoms as long as you follow the license terms. Under the following terms: Attribution — You must give appropriate credit, provide a link to the license, and indicate if changes were made. You may do so in any reasonable manner, but not in any way that suggests the licensor endorses you or your use. No additional restrictions You may not apply legal terms or technological measures that legally restrict others from doing anything the license permits
Editor in Chief
Zhilin Li (Ph.D. (Applied Mathematics))
Professor of Mathematics, Department of Mathematics, North Carolina State University, Raleigh, NC 27695-8205 USA

Bibliography

Prof. Dr. Zhilin Li is associated with Department of Mathematics, North Carolina State University, US since 1997. He was graduated from Nanking Normal University (Mathematics B.S.) in 1982. Whereas, he has completed his Master in Mathematics from University of Washington Applied in 1991. The University of Washington awarded him PhD in Applied Mathematics in 1994. He has published 127 quality manuscript since October 31, 2016. Moreover, he received the Research Grants Current and past from NSF, NIH, NSF/NIGMS, ARO, AFOSR, Oak Ridge, DOE/ARO etc. He is collaborated and affiliated with Juan Alvares, UAH, Spain; Philippe Angot, Aix-Marceille University, France; J. Chen & H. Ji, NNU, China; K Ito, SR Lubkin, NCSU; M-C Lai, Taiwan; R. Luo, UCI; J. Xia, Purdue; Hayk Mikayelyan, Nottingham. Moreover, he has advised and supervised more than 15 graduated students to complete their research projects.

Journal Highlights
Abbreviation: Adv Calc Anal
doi: http://dx.doi.org/10.21065/25205951 
Current Volume: 2 (2017)
Next volume: December, 2018 (Volume 3)
Back volumes: 1
Starting year: 2016
Nature: Online
Submission: Online
Language: English

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Subject & Scope
  • Applied mathematics
  • Bioinformatics
  • Statistical analysis
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  • Compartment and module analysis
  • Algebraic Topology
  • BCK Algebra
  • Semi Rings
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  • Group Theory and Algebraic Modeling
  • Industrial Mathematics
  • Radical Theory of Rings
  • Real Analysis, Algebra
  • Complete Analysis and Differential Geometry
  • Mechanics
  • Topology and Functional Analysis
  • Advanced Analysis
  • Methods of Mathematical Physics
  • Numerical Analysis
  • Mathematical Statistics
  • Computer Applications
  • Group Theory
  • Rings and Modules
  • Number Theory
  • Fluid Mechanics
  • Quantum Mechanics
  • Special Theory of Relatity and Analytical Mechanics
  • Electromagnetic Theory
  • Operations Research
  • Theory of Approimation and Splines
  • Advanced Functional Analysis
  • Solid Mechanics
  • Theory of Optimization

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