and efficient estimators under various statistical models; see, for example, Ghosh and Basu (2013, 2016, 2018) and, in particular, the recent paper by Castilla et al (2019) which discussed a PLR model but under the simple random sampling scheme.

We first start with the mathematical description of the PLR model with complex survey set-up and a brief discussion about the maximum quasi weighted likelihood estimator of the underlying parameters in Section \[sec:MLE\]. Then we introduce a class of new robust parameter estimates for the PLR model with complex survey by minimizing a suitably defined DPD measure in Section \[sec3\]. The asymptotic distribution of the resulting estimator and the design effect for the PLR model with complex survey are also described there. In Section \[secWald\], a new family of Wald-type tests is introduced based on our new estimators for testing linear hypotheses about the parameters of the PLR model. In Section \[sec4\] we theoretically study the robustness of the proposed estimators and Wald-type tests through the influence function analysis. After presenting an illustrative example in Section \[secEx\], an extensive simulation study is presented in Section \[sec5\]. The paper ends with a brief concluding remark in Section \[secCon\]. For brevity in presentation, 