Robust inference for estimating equations with nonignorably missing data based on SIR algorithm

Sampling Importance Resampling Algorithm with Nonignorable Missing Response Variable Based on Smoothed Quantile Regression

“…Common parameter working models are based on linear regression for observed data. Song et al's [21] simulation results showed that model misspecification does not lead to estimation bias. However, their simulation study was based on a regression model that satisfied the Gauss-Markov assumption, with missing response variables following a normal distribution with homoscedasticity concerning the covariates.…”

“…However, nonparametric estimation methods may suffer from the curse of dimensionality when the dimension of the covariates is high. Paik and Larsen [19] proposed using importance resampling to obtain Monte Carlo estimates of conditional means, and Song et al [21] further applied this method to estimation equations. In this study, we extend these methods to quantile regression and overcome the theoretical and computational challenges caused by the nonsmoothness of the checking function in classical quantile regression by employing convolution smoothing.…”

“…Utilizing estimation equations, Paik and Larsen [19] incorporated a working model for observed data and employed a sampling importance resampling (SIR) algorithm to estimate the missing data and corresponding estimation equations. Building upon this, Wang et al [20] and Song et al [21] extended the logistic response model used in the aforementioned approaches to a develop a semiparametric exponential tilt model. However, in the absence of knowledge about the tilting parameter, these methods relied on validation samples.…”