### Abstract

Tang et al. (2003)considered a regression model with missing response, where the missingness mechanism depends on the value of the response variable and hence is nonignorable. They proposed three pseudolikelihood estimators, based on different treatments of the probability distribution of the completely observed covariates. The first assumes the distribution of the covariate to be known, the second estimates this distribution parametrically, and the third estimates the distribution nonparametrically. While it is not hard to show that the second estimator is more efficient than the first,Tang et al. (2003)only conjectured that the third estimator is more efficient than the first two. In this paper, we investigate the asymptotic behaviour of the third estimator by deriving a closed-form representation of its asymptotic variance. We then prove that the third estimator is more efficient than the other two. Our result can be straightforwardly applied to missingness mechanisms that are more general than that inTang et al. (2003).

Original language | English (US) |
---|---|

Pages (from-to) | 479-486 |

Number of pages | 8 |

Journal | Biometrika |

Volume | 105 |

Issue number | 2 |

DOIs | |

State | Published - Jun 1 2018 |

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### All Science Journal Classification (ASJC) codes

- Statistics and Probability
- Mathematics(all)
- Agricultural and Biological Sciences (miscellaneous)
- Agricultural and Biological Sciences(all)
- Statistics, Probability and Uncertainty
- Applied Mathematics

### Cite this

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*Biometrika*, vol. 105, no. 2, pp. 479-486. https://doi.org/10.1093/biomet/asy007

**Optimal pseudolikelihood estimation in the analysis of multivariate missing data with nonignorable nonresponse.** / Zhao, Jiwei; Ma, Yanyuan.

Research output: Contribution to journal › Article

TY - JOUR

T1 - Optimal pseudolikelihood estimation in the analysis of multivariate missing data with nonignorable nonresponse

AU - Zhao, Jiwei

AU - Ma, Yanyuan

PY - 2018/6/1

Y1 - 2018/6/1

N2 - Tang et al. (2003)considered a regression model with missing response, where the missingness mechanism depends on the value of the response variable and hence is nonignorable. They proposed three pseudolikelihood estimators, based on different treatments of the probability distribution of the completely observed covariates. The first assumes the distribution of the covariate to be known, the second estimates this distribution parametrically, and the third estimates the distribution nonparametrically. While it is not hard to show that the second estimator is more efficient than the first,Tang et al. (2003)only conjectured that the third estimator is more efficient than the first two. In this paper, we investigate the asymptotic behaviour of the third estimator by deriving a closed-form representation of its asymptotic variance. We then prove that the third estimator is more efficient than the other two. Our result can be straightforwardly applied to missingness mechanisms that are more general than that inTang et al. (2003).

AB - Tang et al. (2003)considered a regression model with missing response, where the missingness mechanism depends on the value of the response variable and hence is nonignorable. They proposed three pseudolikelihood estimators, based on different treatments of the probability distribution of the completely observed covariates. The first assumes the distribution of the covariate to be known, the second estimates this distribution parametrically, and the third estimates the distribution nonparametrically. While it is not hard to show that the second estimator is more efficient than the first,Tang et al. (2003)only conjectured that the third estimator is more efficient than the first two. In this paper, we investigate the asymptotic behaviour of the third estimator by deriving a closed-form representation of its asymptotic variance. We then prove that the third estimator is more efficient than the other two. Our result can be straightforwardly applied to missingness mechanisms that are more general than that inTang et al. (2003).

UR - http://www.scopus.com/inward/record.url?scp=85048660131&partnerID=8YFLogxK

UR - http://www.scopus.com/inward/citedby.url?scp=85048660131&partnerID=8YFLogxK

U2 - 10.1093/biomet/asy007

DO - 10.1093/biomet/asy007

M3 - Article

C2 - 30799873

AN - SCOPUS:85048660131

VL - 105

SP - 479

EP - 486

JO - Biometrika

JF - Biometrika

SN - 0006-3444

IS - 2

ER -