Parametric inference for proportional (reverse) hazard rate models with nomination sampling

\noindent Randomized nomination sampling (RNS) is a rank-based sampling technique which has been shown to be effective in several nonparametric studies involving environmental and ecological applications. In this paper, we investigate parametric inference using RNS design for estimating the unknown vector of parameters $\boldsymbol{\theta}$ in the proportional hazard rate and proportional reverse hazard rate models. We examine both maximum likelihood (ML) and method of moments (MM) methods and investigate the relative precision of our proposed RNS-based estimators compared with those based on simple random sampling (SRS). We introduce four types of RNS-based data as well as necessary EM algorithms for the ML estimation, and evaluate the performance of corresponding estimators in estimating $\boldsymbol{\theta}$. We show that there are always values of the design parameters on which RNS-based estimators are more efficient than those based on SRS. Inference based on imperfect ranking is also explored and it is shown that the improvement holds even when the ranking is imperfect. Theoretical results are augmented with numerical evaluations and a case study.