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Quasi-Likelihood Estimation of a Censored Autoregressive Model With Exogenous Variables

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  • Chao Wang
  • Kung-Sik Chan

Abstract

Maximum likelihood estimation of a censored autoregressive model with exogenous variables (CARX) requires computing the conditional likelihood of blocks of data of variable dimensions. As the random block dimension generally increases with the censoring rate, maximum likelihood estimation becomes quickly numerically intractable with increasing censoring. We introduce a new estimation approach using the complete-incomplete data framework with the complete data comprising the observations were there no censoring. We introduce a system of unbiased estimating equations motivated by the complete-data score vector, for estimating a CARX model. The proposed quasi-likelihood method reduces to maximum likelihood estimation when there is no censoring, and it is computationally efficient. We derive the consistency and asymptotic normality of the quasi-likelihood estimator, under mild regularity conditions. We illustrate the efficacy of the proposed method by simulations and a real application on phosphorus concentration in river water.

Suggested Citation

  • Chao Wang & Kung-Sik Chan, 2018. "Quasi-Likelihood Estimation of a Censored Autoregressive Model With Exogenous Variables," Journal of the American Statistical Association, Taylor & Francis Journals, vol. 113(523), pages 1135-1145, July.
  • Handle: RePEc:taf:jnlasa:v:113:y:2018:i:523:p:1135-1145
    DOI: 10.1080/01621459.2017.1307115
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    Cited by:

    1. Negahban, Ashkan, 2019. "Simulation-based estimation of the real demand in bike-sharing systems in the presence of censoring," European Journal of Operational Research, Elsevier, vol. 277(1), pages 317-332.
    2. Harvey, A. & Liao, Y., 2019. "Dynamic Tobit models," Cambridge Working Papers in Economics 1913, Faculty of Economics, University of Cambridge.
    3. Harvey, Andew & Liao, Yin, 2023. "Dynamic Tobit models," Econometrics and Statistics, Elsevier, vol. 26(C), pages 72-83.

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