Virtual Graduation Ceremony

45th Graduation Ceremony

PhD in STATISTICS


Nonparametric Model-Calibration Estimation of Finite Population Total in Complex Survey

Abstract: Nonparametric methods are rich classes of statistical tools that have gained acceptance in most areas of statistics. Researchers have used them to fit missing values in the presence of auxiliary variables in sampling surveys where missing values denote non-sampled, non-response or even non-observed. Nonparametric methods have been preferred to parametric methods since they make it possible to analyze data, estimate trends and conduct inference without fully specifying a parametric model for the data. This study, therefore, presented some new attempts towards imputation of missing values and using auxiliary information effectively in nonparametric techniques, namely, penalized splines and Artificial neural networks in complex surveys. More precisely, the study adopted Artificial Neural Network learning and penalized splines for estimating the functional relationship between the survey variable and the auxiliary variables. In particular, the study extended model calibration by penalty function by assuming more general population models and employed nonparametric methods to obtain the fitted values to calibrate on. The penalty function is used to derive nonparametric model calibrated estimators by treating the calibration problem as a nonlinearly constrained minimization problem, which is transformed into an unconstrained optimization problem. Artificial Neural networks and penalized splines have already been employed in survey sampling as an imputation technique; however, their application for model calibration is new in complex survey data. This complex survey data was sampled through cluster-strata design, which involved a population divided into clusters which are further subdivided into strata. A Monte Carlo simulation was run to assess the finite sample performance of the estimators under complex survey data. The MSE criterion was used to check the efficiency of the estimator’s performance. This work contributes to the literature in three ways. First, it derived an estimator of population total using model calibration on nonparametric techniques, penalized splines and Artificial Neural Network methods. Secondly, it established the theoretical properties, such as the design unbiasedness of the population estimator. Finally, it established empirical properties of the population total estimator using simulated data. This research concludes that both model calibrated estimators based on the Penalized spline and Artificial Neural Network are competitively efficient estimators since they yield smaller estimation errors compared to the design estimator; Horvitz Thompson (HT). Thus, the study is expected to be applied in places like micro-econometrics to provide the researchers with better population parameter estimates through a model calibration approach based on the Artificial Neural Networks and penalized splines.

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