Parametric likelihood inference and goodness-of-fit for dependently left-truncated data, a copula-based approach

Statistical Papers volume 61, pages479–501(2020)Cite this article

Abstract

Traditionally, the literature on statistical inference with left-truncated samples assumes the independence of truncation variable on lifetime. Alternatively, this paper considers an approach of using a copula for dependent truncation. When considering maximum likelihood estimation and goodness-of-fit procedures, key challenges are the absence of the explicit form of the inclusion probability and truncated distribution functions. This paper shows that, under the copula model, the inclusion probability and truncated distribution functions are expressed as univariate integrals of some functions. With aid of these expressions, we propose computational algorithms to maximize the log-likelihood and to perform goodness-of-fit tests. Simulations are conducted to examine the performance of the proposed method. Real data from a field reliability study on the brake pad lifetimes are analyzed for illustration. Relevant computational programs are made available in the R package “depend.truncation”.

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Acknowledgements

The authors thank two anonymous reviewers for their helpful comments that improved the paper. This work is supported by the Research Grants funded by the Government of Taiwan (MOST 103-2118-M-008-MY2; MOST 105-2118-M-008-003-MY2).

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Affiliations

  1. Graduate Institute of Statistics, National Central University, No. 300, Zhongda Rd., Zhongli District, Taoyuan City, 32001, Taiwan

    Takeshi Emura & Chi-Hung Pan

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  1. Takeshi Emura
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  2. Chi-Hung Pan
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Correspondence to Takeshi Emura.

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Emura, T., Pan, C. Parametric likelihood inference and goodness-of-fit for dependently left-truncated data, a copula-based approach. Stat Papers 61, 479–501 (2020). https://doi.org/10.1007/s00362-017-0947-z

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Keywords

  • Bivariate life distribution
  • Goodness-of-fit test
  • Newton–Raphson algorithm
  • Reliability
  • Survival analysis
  • Left-truncation
  • Weibull distribution