Signed-rank regression inference via empirical likelihood

Abstract

For the general stochastic regression analysis of complete data, Bindele and Abebe [Bounded influence nonlinear signed-rank regression. Can J Stat. 2012;40(1):172-189. Available from: http://dx.doi.org/10.1002/cjs.10134 ] proposed the signed-rank (SR) estimator. However, there exists an over-coverage problem for the confidence intervals of the regression parameters when the sample size is small. In this paper, we investigate an empirical likelihood (EL) approach to construct confidence intervals for the regression parameters based on the SR estimating equation. The limiting distribution of log-empirical likelihood ratio is χ 2 distribution. We carry out extensive simulation studies to compare the proposed method with the normal approximation-based method. The simulation results show that the proposed method outperforms the existing method in terms of the coverage probability and average length of confidence intervals. We illustrate the EL method using a real data example.

Rank-based estimating equation with non-ignorable missing responses via empirical likelihood

“…The covariate x is generated from N (1, 1) and δ is generated from a Bernoulli distribution with response probability π(x, y). To acomodate a nonlinear case, as in Bindele & Zhao (2016), we also consider the Micheaelis-Menten function defined as g(x, β) = x/(β + x), where the true β = 1, x is generated from an exponential distribution, and the random errors are generated just from CN (0.9) and t 3 for the sake of brevity. We investigate five different response probability cases:…”

“…Qin & Lawless (1994) developed the EL inference procedure for general estimating equations for complete data, and Owen (2001) makes an excellent summary about the theory and applications of the EL methods. Recent progress in the EL method includes linear transformation models with right censoring ), Yang & Zhao (2012), the jackknife EL procedure (Jing et al (2009), Gong et al (2010, Zhang & Zhao (2013), ), high dimensional EL method (Chen et al (2009), Hjort et al (2009), Tang & Leng (2010, Lahiri et al (2012)), and the signedrank regression (Bindele & Zhao, 2016). More recently, in the context of missing response under the MNAR assumption, empirical likelihood approaches have been proposed by Niu et al (2014) and Tang et al (2014).…”