The Signed-rank estimator for nonlinear regression with responses missing at random

Abstract

This paper is concerned with the study of the signed-rank estimator of the regression coefficients under the assumption that some responses are missing at random in the regression model. Strong consistency and asymptotic normality of the proposed estimator are established under mild conditions. To demonstrate the performance of the signed-rank estimator, a simulation study is conducted under different settings of model error’s distributions, and shows that the proposed estimator is more efficient than the least squares estimator whenever the error distribution is heavy-tailed or contaminated. When the model error follows a normal distribution, the simulation experiment shows that the signed-rank estimator is more efficient than its least squares counterpart whenever a large proportion of the responses are missing.