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Robust analysis of semiparametric renewal process models.
Feng-Chang Lin1, Young K Truong1, Jason P Fine1
1Department of Biostatistics, University of North Carolina, Chapel Hill, North Carolina 27599, U.S.A.
Biometrika
|February 20, 2014
Summary
This study introduces a rate model for analyzing sequential data, offering a more robust approach than standard intensity models when dependencies exist. The proposed method improves statistical inference for complex time-series data, including neural spike trains.
Area of Science:
- Statistics
- Time Series Analysis
- Biostatistics
Background:
- Standard intensity models may fail to capture dependencies in sequential data.
- Renewal processes are crucial for modeling event sequences.
- Semiparametric models are widely used but often assume data independence.
Purpose of the Study:
- To propose and validate a semiparametric multiplicative rate model for modulated renewal processes.
- To address challenges in statistical inference for dependent sequential data.
- To compare the utility of the rate model against the intensity model for time-series analysis.
Main Methods:
- Utilizing partial likelihood-based inferences under a semiparametric multiplicative rate model.
- Applying limit theory for stationary sequences with mixing conditions.
- Adapting block bootstrapping and cluster variance estimators for complex variance estimation.
Main Results:
- Demonstrated consistency and asymptotic normality of the proposed estimator.
- Developed methods to handle the complicated variance estimation due to unknown gap time dependencies.
- Simulation studies confirmed the practical utility of the rate model.
Conclusions:
- The proposed rate model offers a more effective approach for analyzing modulated renewal processes with dependent sequences.
- The developed statistical inference methods are practical and outperform traditional intensity models in specific scenarios.
- This work has implications for analyzing neural spike train data and other time-series applications.
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