Nonparametric Penalized Spline Model Calibrated Estimator in Complex Survey with Known Auxiliary Information at Both Cluster and Element Levels

The present study uses penalized splines (p- spline) to estimate the functional relationship between the survey variable and the auxiliary variable in a complex survey design; where a population divided into clusters is in turn subdivided into strata. This study has considered a case of auxiliary information present at two levels; at both cluster and element levels. The study further, applied model calibration technique by penalty function to estimate population total. The calibration problems at both levels have been treated as optimization problems and solving by the method of penalty functions so as to derive the estimators for this study. The reasoning behind the use of model calibration is that if the calibration constraints are satisfied by the auxiliary variable, then the study expects that the fitted values of the variable of interest satisfies such constraints too. This study run a Monte Carlo simulation to assess the finite sample performance of the penalized spline model calibrated estimator under complex survey data. Simulation studies were conducted to compare the efficiency of p-spline model calibrated estimator with Horvitz Thompson estimator (HT) by mean squared error (MSE) criterion. This study shows that the p-spline model-based estimator is generally more efficient than the HT in terms of the mean squared error. The results have also shown that the estimator obtained is unbiased, consistent and very robust because it does not fail in the event the model is misspecified for the data.