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Regression Analysis of Doubly Truncated Data.

Zhiliang Ying1, Wen Yu2, Ziqiang Zhao3

  • 1Department of Statistics, Columbia University, New York.

Journal of the American Statistical Association
|September 21, 2020
PubMed
Summary
This summary is machine-generated.

This study introduces a new nonparametric method for analyzing doubly truncated data, common in astronomy and econometrics. The method extends rank estimators for improved regression parameter estimation and is validated with real-world datasets.

Keywords:
Confidence intervalEmpirical processL1 methodLinear programmingRank estimationResamplingU-processWilcoxon-Mann-Whitney Statistic

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Area of Science:

  • Statistics
  • Econometrics
  • Astronomy
  • Survival Analysis

Background:

  • Doubly truncated data, where observations are confined to specific intervals, pose significant analytical challenges.
  • Existing methods for one-sided truncation are insufficient for doubly truncated data.
  • Previous nonparametric approaches for doubly truncated data include those by Efron and Petrosian (1999).

Purpose of the Study:

  • To propose a general nonparametric method for estimating regression parameters with doubly truncated dependent variables.
  • To extend existing rank-based estimators to handle double truncation.
  • To provide a computationally accessible method for analyzing such data.

Main Methods:

  • Development of a general nonparametric method extending the Mann-Whitney-type rank estimator.
  • Incorporation of weighted rank estimation for enhanced efficiency.
  • Utilizing resampling schemes for approximating limiting distributions.

Main Results:

  • The proposed estimators are demonstrated to be consistent and asymptotically normal.
  • The method extends existing rank estimators and is easily computable.
  • Analysis of quasar and AIDS incubation data using the new method.

Conclusions:

  • The new method offers a robust approach for analyzing doubly truncated data across various scientific fields.
  • The proposed technique is computationally efficient and statistically sound.
  • Simulation results confirm the efficacy of the developed method for regression parameter estimation.