Nonparametric prediction distribution from resolution-wise regression with heterogeneous data
Jialu Li1, Wan Zhang2, Peiyao Wang2
1School of Mathematics and Statistics, Beijing Institute of Technology, Beijing 100081, China.
Journal of Business & Economic Statistics : a Publication of the American Statistical Association
|December 4, 2023
Summary
This study introduces a new nonparametric regression method for heterogeneous data, providing response distributions instead of single values. The approach effectively handles complex data patterns and offers consistent performance, even with increasing dimensions.
Area of Science:
- Statistics
- Machine Learning
- Data Science
Background:
- Heterogeneous data modeling is crucial for personalized marketing.
- Existing regression methods often focus on conditional means and may need cluster information.
- Addressing data heterogeneity requires advanced statistical approaches.
Purpose of the Study:
- To propose a novel nonparametric resolution-wise regression procedure.
- To estimate the full distribution of the response, not just a single value.
- To accommodate data heterogeneity without requiring prior cluster information.
Main Methods:
- Decomposing response and predictor information into resolutions and patterns using marginal binary expansions.
- Modeling relationships between resolutions and patterns via penalized logistic regressions.
- Constructing a conditional response histogram to approximate the distribution.
Main Results:
- The proposed method provides an estimated distribution of the response.
- Demonstrates a sure independence screening property.
- Exhibits consistency for growing dimensions.
- Effectiveness validated through simulations and a real estate dataset.
Conclusions:
- The resolution-wise regression offers a powerful tool for modeling heterogeneous data.
- It provides a more comprehensive understanding of response variability compared to traditional methods.
- The method is robust and scalable for high-dimensional applications.
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