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Inversion Theorem Based Kernel Density Estimation for the Ordinary Least Squares Estimator of a Regression
Dongliang Wang1, Alan D Hutson2
1Department of Public Health and Preventive Medicine, State University of New York Upstate Medical University, Syracuse, New York, USA.
Communications in Statistics: Theory and Methods
|March 1, 2016
Summary
This study introduces a new kernel density estimator for ordinary least squares regression, improving confidence interval power for small sample sizes and non-normal data.
Area of Science:
- Statistics
- Econometrics
- Data Science
Background:
- Ordinary least squares (OLS) regression confidence intervals are unreliable with non-normal data.
- Existing methods struggle with small sample sizes, impacting statistical power.
Purpose of the Study:
- To develop a robust kernel density estimator for OLS coefficients.
- To improve the accuracy and power of confidence intervals in challenging data conditions.
Main Methods:
- Utilized kernel smoothing and inversion techniques for density estimation.
- Developed a novel kernel density estimator tailored for OLS.
- Estimated conditional probability density distributions.
Main Results:
- The proposed method significantly enhances statistical power compared to Wald-type confidence intervals.
- Demonstrated superior performance with small sample sizes and non-normal distributions.
Conclusions:
- The novel kernel density estimator offers a more reliable approach for OLS confidence intervals.
- Effective for small, non-normal datasets, improving statistical inference.
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