Random nonlinear model with missing responses

TL;DR

This paper investigates empirical likelihood methods for nonlinear models with missing responses, demonstrating improved coverage accuracy and valid asymptotic distributions through theoretical analysis and simulations.

Contribution

It introduces empirical likelihood ratio techniques for nonlinear models with missing data, establishing their asymptotic properties and demonstrating superior coverage over normal approximation methods.

Findings

EL methods outperform normal approximation in coverage probability

Asymptotic chi-squared distribution holds for EL statistics with different estimators

Empirical log-likelihood remains valid on imputed data

Abstract

A nonlinear model with response variable missing at random is studied. In order to improve the coverage accuracy, the empirical likelihood ratio (EL) method is considered. The asymptotic distribution of EL statistic and also of its approximation is $\chi^2$ if the parameters are estimated using least squares(LS) or least absolute deviation(LAD) method on complete data. When the response are reconstituted using a semiparametric method, the empirical log-likelihood associated on imputed data is also asymptotically $\chi^2$. The Wilk's theorem for EL for parameter on response variable is also satisfied. It is shown via Monte Carlo simulations that the EL methods outperform the normal approximation based method in terms of coverage probability up to and including on the reconstituted data. The advantages of the proposed method are exemplified on the real data.