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Improved confidence interval for average annual percent change in trend analysis
Hyune-Ju Kim1, Jun Luo2, Huann-Sheng Chen3
1Department of Mathematics, Syracuse University, Syracuse, 13244, New York, U.S.A.
Statistics in Medicine
|June 7, 2017
Summary
This study introduces an improved confidence interval for average annual percent change in trend analysis, enhancing segmented regression models. New methods offer simpler construction and better performance using t-distribution and empirical resampling.
Area of Science:
- Statistics
- Econometrics
- Time Series Analysis
Background:
- Trend analysis is crucial for understanding long-term changes.
- Segmented line regression models identify significant shifts in trends.
- Accurate confidence intervals are essential for reliable trend interpretation.
Purpose of the Study:
- To propose and evaluate an improved confidence interval for the average annual percent change in trend analysis.
- To enhance the performance of segmented line regression models with unknown change points.
- To introduce two novel methods for improving confidence interval accuracy.
Main Methods:
- Weighted average of regression slopes in segmented line regression.
- Modification of Muggeo's confidence interval using the t-distribution.
- Empirical distribution of residuals with uniform random sample resampling.
Main Results:
- The proposed confidence interval demonstrates improved performance.
- A simpler construction method is presented, equivalent to Muggeo's approach.
- The second method, based on empirical distribution and resampling, shows satisfactory performance in simulations.
Conclusions:
- The developed methods provide more accurate confidence intervals for trend analysis.
- These improvements enhance the reliability of detecting and quantifying changes in trends.
- The study contributes to more robust statistical modeling in time series analysis.
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