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Semiparametric inference on general functionals of two semicontinuous populations

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Abstract

In this paper, we propose new semiparametric procedures for inference on linear functionals in the context of two semicontinuous populations. The distribution of each semicontinuous population is characterized by a mixture of a discrete point mass at zero and a continuous skewed positive component. To utilize the information from both populations, we model the positive components of the two mixture distributions via a semiparametric density ratio model. Under this model setup, we construct the maximum empirical likelihood estimators of the linear functionals. The asymptotic normality of the proposed estimators is established and is used to construct confidence regions and perform hypothesis tests for these functionals. We show that the proposed estimators are more efficient than the fully nonparametric ones. Simulation studies demonstrate the advantages of our method over existing methods. Two real-data examples are provided for illustration.

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Acknowledgements

The authors thank the Chief Editor, the Associate Editor, and two reviewers for their very careful reading and a number of helpful comments. The authors are grateful to Dr. Changbao Wu for his constructive and helpful comments. Dr. Wang’s work is supported in part by National Natural Science Foundation of China Grants 12001454, 11971404, Humanities and Social Sciences Foundation of the Ministry of Education of China Grant 19YJC910005, and Natural Science Foundation of Fujian Province Grant 2020J01031. Dr. Li’s work is supported in part by the Natural Sciences and Engineering Research Council of Canada Grant RGPIN-2020-04964.

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Authors and Affiliations

  1. Department of Statistics and Actuarial Science, University of Waterloo, 200 University Avenue West, Waterloo, ON, N2L 3G1, Canada

    Meng Yuan & Pengfei Li

  2. Department of Statistics, School of Economics, Wang Yanan Institute for Studies in Economics, MOE Key Lab of Econometrics and Fujian Key Lab of Statistics, Xiamen University, 422 Siming South Road, Xiamen, 361005, Fujian, China

    Chunlin Wang

  3. Dalla Lana School of Public Health, University of Toronto, 155 College Street, Toronto, ON, M5T 3M7, Canada

    Boxi Lin

Authors
  1. Meng Yuan
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  2. Chunlin Wang
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  3. Boxi Lin
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  4. Pengfei Li
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Correspondence to Chunlin Wang.

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Yuan, M., Wang, C., Lin, B. et al. Semiparametric inference on general functionals of two semicontinuous populations. Ann Inst Stat Math 74, 451–472 (2022). https://doi.org/10.1007/s10463-021-00804-4

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  • DOI: https://doi.org/10.1007/s10463-021-00804-4

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