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Nonparametric estimation for big-but-biased data

Author

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  • Laura Borrajo

    (CITIC, University of A Coruña)

  • Ricardo Cao

    (CITIC and ITMATI, University of A Coruña)

Abstract

Nonparametric estimation for a large-sized sample subject to sampling bias is studied in this paper. The general parameter considered is the mean of a transformation of the random variable of interest. When ignoring the biasing weight function, a small-sized simple random sample of the real population is assumed to be additionally observed. A new nonparametric estimator that incorporates kernel density estimation is proposed. Asymptotic properties for this estimator are obtained under suitable limit conditions on the small and the large sample sizes and standard and non-standard asymptotic conditions on the two bandwidths. Explicit formulas are shown for the particular case of mean estimation. Simulation results show that the new mean estimator outperforms two classical ones for suitable choices of the two smoothing parameters involved. The influence of two smoothing parameters on the performance of the final estimator is also studied, exhibiting a striking limit behavior of their optimal values. The new method is applied to a real data set from the Telco Company Vodafone ES, where a bootstrap algorithm is used to select the smoothing parameter.

Suggested Citation

  • Laura Borrajo & Ricardo Cao, 2021. "Nonparametric estimation for big-but-biased data," TEST: An Official Journal of the Spanish Society of Statistics and Operations Research, Springer;Sociedad de Estadística e Investigación Operativa, vol. 30(4), pages 861-883, December.
    • Handle: RePEc:spr:testjl:v:30:y:2021:i:4:d:10.1007_s11749-020-00749-5
    DOI: 10.1007/s11749-020-00749-5
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    References listed on IDEAS

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    1. Montanari, Giorgio E. & Ranalli, M. Giovanna, 2005. "Nonparametric Model Calibration Estimation in Survey Sampling," Journal of the American Statistical Association, American Statistical Association, vol. 100, pages 1429-1442, December.
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    3. Ma, Yanyuan & Genton, Marc G. & Tsiatis, Anastasios A., 2005. "Locally Efficient Semiparametric Estimators for Generalized Skew-Elliptical Distributions," Journal of the American Statistical Association, American Statistical Association, vol. 100, pages 980-989, September.
    4. Yanyuan Ma & Mijeong Kim & Marc G. Genton, 2013. "Semiparametric Efficient and Robust Estimation of an Unknown Symmetric Population Under Arbitrary Sample Selection Bias," Journal of the American Statistical Association, Taylor & Francis Journals, vol. 108(503), pages 1090-1104, September.
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