Semiparametric likelihood for estimating equations with non-ignorable non-response by non-response instrument

ABSTRACT

Non-response or missing data is a common phenomenon in many areas. Non-ignorable non-response, a response mechanism that depends on the values of the variable having non-response, is the most difficult type of non-response to handle. This paper considers statistical inference of unknown parameters in estimating equations (EEs) when the variable of interest has non-ignorable non-response. By utilising the cutting edge techniques of non-response instrument, a parametric response propensity function can be identified and estimated. Then a semiparametric likelihood is constructed with the propensity function, EEs and auxiliary information being incorporated into the constraints to make the inference valid and improve the estimation efficiency. Asymptotic distributions for the resulting parameter estimates are derived. Empirical results including two simulation studies and a real example show that the proposed method gives promising results.

KEYWORDS:

• Auxiliary information
• empirical likelihood
• generalised method of moments
• missing not at random
• non-response instrument

AMS SUBJECT CLASSIFICATIONS:

• 62F12
• 62G30

Disclosure statement

No potential conflict of interest was reported by the authors.

Additional information

Funding

Fang Fang's research was partially supported by National Natural Science Foundation of China [11831008, 11601156].