Semiparametric estimation of copula models with nonignorable missing data

Abstract

This paper investigates the estimation of parametric copula models when the data have nonignorable nonresponse. We consider the propensity follows a general semiparametric model, but the distribution of the response variable and related covariates is unspecified. To solve the identifiability problem, we use an instrumental covariate, which is related to the response variable but unrelated to the propensity given the response variable and other covariates. The generalised method of moments is applied to estimate the parameters in the propensity. Based on kernel-assisted regression approach, we construct the bias-corrected semiparametric estimating equations to improve estimation efficiency. Consistency and asymptotic normality of the proposed estimators are established. The finite-sample performance of the estimators is studied through simulation, and an application to HIV-CD4 data set is also presented.

Keywords:

• Copula
• kernel-assisted regression
• identifiability
• missing not at random
• nonresponse instrument

AMS Subject Classifications:

• 62G05
• 62G20

Acknowledgments

We are grateful to the Editor, the associate editor and two anonymous referees for their insightful comments and suggestions, which have led to significant improvements.

Disclosure statement

No potential conflict of interest was reported by the authors.

Additional information

Funding

Our research was supported by the National Natural Science Foundation of China (11871287, 11501208), the Natural Science Foundation of Tianjin (18JCYBJC41100), the Fundamental Research Funds for the Central Universities, the Key Laboratory for Medical Data Analysis and Statistical Research of Tianjin.