We introduce a new sufficient statistic for the population parameter vector by allowing for the sampling design to first be selected at random amongst a set of candidate sampling designs. In contrast to the traditional approach in survey sampling, we
achieve this by defining the observed data to include a mention of the sampling design used for the data collection aspect of the study. We show that the reduced data consisting of the unit labels together with their corresponding responses of interest is a sufficient statistic under this setup. A Rao-Blackwellization inference procedure is outlined and it is shown how averaging over hypothetical observed data outcomes results in improved estimators; the improved strategy includes considering all possible sampling designs in the candidate set that could have given rise to the reduced data. Expressions for the variance of the Rao-Blackwell estimators are also derived. The results from two simulation studies are presented to demonstrate the practicality of our approach. A discussion on how our approach can be useful when the analyst has limited information on the data collection procedure is also provided.
A new strategy is introduced for estimating population size and networked population characteristics. Sample selection is based on a multi-wave snowball sampling design. A generalized stochastic block model is posited for the populations network grap
h. Inference is based on a Bayesian data augmentation procedure. Applications are provided to an empirical and simulated populations. The results demonstrate that statistically efficient estimates of the size and distribution of the population can be achieved.
We investigate a Poisson sampling design in the presence of unknown selection probabilities when applied to a population of unknown size for multiple sampling occasions. The fixed-population model is adopted and extended upon for inference. The compl
ete minimal sufficient statistic is derived for the sampling model parameters and fixed-population parameter vector. The Rao-Blackwell version of population quantity estimators is detailed. An application is applied to an emprical population. The extended inferential framework is found to have much potential and utility for empirical studies.
We explore the use of a sufficient statistic based on the identified members that are obtained for samples that are selected under the $M_0$ capture-recapture closed population model (Schwarz and Seber, 1999). A Rao-Blackwellized version of the estim
ator based on a sufficient statistic is then presented. We explore the efficiency of the improved estimator via a simulation study. The R code for the simulation is provided in the appendix.
We explore the use of a sufficient statistic based on the data of samples that are selected under the M_0 capture-recapture closed population model (Schwarz and Seber, 1999). A Rao-Blackwellized version of the estimator based on a sufficient statisti
c is then presented. Though the improvements made on the preliminary capture-recapture estimates are likely to be negligible, this body of work is primarily intended to contribute to the theory around the capture-recapture models. The code for a simulation is provided in the appendix.
We present a new design and inference method for estimating population size of a hidden population best reached through a link-tracing design. The strategy involves the Rao-Blackwell Theorem applied to a sufficient statistic markedly different from t
he usual one that arises in sampling from a finite population. An empirical application is described. The result demonstrates that the strategy can efficiently incorporate adaptively selected members of the sample into the inference procedure.
