Improved pseudo maximum likelihood estimation for survey data

The pseudo maximum likelihood (PML) method is widely used in survey data analysis. In this paper, we modify sampling probabilities using a thresholding method and propose an improved pseudo maximum likelihood (IPML) estimation for generalized linear models. The proposed IPML estimator is design consistent with the maximum likelihood estimator derived from the finite population, and it satisfies asymptotic normality. We compare the efficiency of IPML and PML estimators in terms of their asymptotic covariance matrix. Some theoretical results of the IPML estimator under linear and logistic models are discussed in the paper. Additionally, we develop an improved model-assisted (IMA) estimation based on the generalized linear superpopulation models. The theoretical properties of the IMA estimator are also derived, and numerical simulations demonstrate that the improved estimators are more efficient than the original estimators.