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
CobbDouglas function is commonly used to describe the linear relationship
between the login puts, such as labor and capital, and the logoutput. However,
this function may not well describe the relationship. To avoid model
misspecification, 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, semiparametric regression models are
introduced. The models include partial linear regression model, single index
model, additive model, varying coe±cient model, and so on. These
semiparametric regression models describe the relationship between the
response and the predictors in a semiparametric 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/nonparametric regression
models, regression models for missing, censored, functional and highdimensional
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 computerbased experiments. Illustrations with
relevant, original data are strongly encouraged when presented with clear
contextual justification and explanation.

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