Semiparametric Model-Assisted Approach to Probabilistic Sampling of Finite Populations With High Right-Skew and Kurtosis

We offer a new semiparametric model-assisted estimator for the total population parameter of an asymmetric finite population. In some practical situations, such as estimating totals of high rigth-skew finite populations or when the auxiliary variables and the interest variable have an unknown nonlinear association, the more traditional assisted estimators, REG and GEREG, may not obtain acceptable results. We propose a novel class of semiparametric model-assisted estimators to solve the mention drawbacks of the REG and GEREG estimators. We suppose a generalized Gamma superpopulation model that generate the finite population and propose a semiparametric model-assisted regression estimator (SREG). Under mild conditions, we study the asymptotic properties of the first-order approximation of the SREG estimator. We show that simple random sampling without replacement (SI), simple random sampling with replacement (SRSWR) using unequal probabilities of selection, Poisson sampling (PO), and stratified sampling with SI (STSI) hold the conditions for a desirable asymptotic behaviour. Nonetheless, simple random sampling with replacement (SRSWR) using equal probabilities of selection and systematic sampling (SY) do not hold the conditions. Additionally, through several Monte Carlo simulations, we assess the performance of SREG estimators and compare it with some natural competitors, HT, REG and Model-Calibration estimators, showing a better behaviour of SREG. Finally, one application is presented in which the SREG estimator shows a satisfactory performance, in contrast of the HT, REG and Model-Calibration estimators.