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A Kolmogorov–Smirnov-type test for the two-sample problem with left-truncated data

Author

Listed:
  • Adrián Lago

    (CITMAga, Universidade de Vigo)

  • Jacobo Uña-Álvarez

    (CITMAga, Universidade de Vigo)

  • Juan Carlos Pardo-Fernández

    (CITMAga, Universidade de Vigo)

Abstract

A Kolmogorov–Smirnov-type test for the two-sample problem with left-truncated data is proposed. The asymptotic null distribution of the test statistic and its omnibus consistency are established. A bootstrap resampling plan to approximate the null distribution of the test statistic is introduced. The finite sample performance of the proposed test is investigated through simulations. Comparison to the well-known log-rank test and a real data illustration are included.

Suggested Citation

  • Adrián Lago & Jacobo Uña-Álvarez & Juan Carlos Pardo-Fernández, 2025. "A Kolmogorov–Smirnov-type test for the two-sample problem with left-truncated data," TEST: An Official Journal of the Spanish Society of Statistics and Operations Research, Springer;Sociedad de Estadística e Investigación Operativa, vol. 34(1), pages 69-90, March.
    • Handle: RePEc:spr:testjl:v:34:y:2025:i:1:d:10.1007_s11749-024-00948-4
    DOI: 10.1007/s11749-024-00948-4
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    References listed on IDEAS

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    1. Anderson, N. H. & Hall, P. & Titterington, D. M., 1994. "Two-Sample Test Statistics for Measuring Discrepancies Between Two Multivariate Probability Density Functions Using Kernel-Based Density Estimates," Journal of Multivariate Analysis, Elsevier, vol. 50(1), pages 41-54, July.
    2. Arcones, Miguel A. & Giné, Evarist, 1995. "On the law of the iterated logarithm for canonical U-statistics and processes," Stochastic Processes and their Applications, Elsevier, vol. 58(2), pages 217-245, August.
    3. Li, Yun-Xia & Wang, Jian-Feng, 2008. "An almost sure central limit theorem for products of sums under association," Statistics & Probability Letters, Elsevier, vol. 78(4), pages 367-375, March.
    4. Zhou, Yong & Yip, Paul S. F., 1999. "A Strong Representation of the Product-Limit Estimator for Left Truncated and Right Censored Data," Journal of Multivariate Analysis, Elsevier, vol. 69(2), pages 261-280, May.
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