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Variance Estimation for Statistics Computed from Single Recurrent Event Processes


  • Yongtao Guan,

    Corresponding author
    1. Division of Biostatistics, Yale University, New Haven, Connecticut 06520, U.S.A.
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  • Jun Yan,

    1. Department of Statistics, University of Connecticut, Storrs, Connecticut 06269, U.S.A.
    2. Institute for Publich Health Research, University of Connnecticut Health Center, East Hartford, Connecticut 06108, U.S.A.
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  • Rajita Sinha

    1. Department of Psychiatry and Child Study Center, Yale University, New Haven, Connecticut 06511, U.S.A.
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Summary This article is concerned with variance estimation for statistics that are computed from single recurrent event processes. Such statistics are important in diagnosis for each individual recurrent event process. The proposed method only assumes a semiparametric form for the first-order structure of the processes but not for the second-order (i.e., dependence) structure. The new variance estimator is shown to be consistent for the target parameter under very mild conditions. The estimator can be used in many applications in semiparametric rate regression analysis of recurrent event data such as outlier detection, residual diagnosis, as well as robust regression. A simulation study and application to two real data examples are used to demonstrate the use of the proposed method.