approaches estimates inclusion probabilities for convenience sample units by specifying reference sample-weighted pseudo … inclusion probabilities for the reference and convenience samples as our main result. Our approach allows specification of a … hierarchical formulation that simultaneously estimates sample propensity scores and the convenience sample inclusion probabilities …

first-order inclusion probabilities only and is usually more accurate than the Hansen-Hurwitz estimator. We review this …-replacement unequal probability designs. This estimator is rarely implemented because of the complexity of determining joint inclusion … probabilities. In practice, the variance is usually estimated by simpler variance estimators such as the Hansen-Hurwitz with …

formula relating inclusion probabilities of adjacent orders can be used to ease computational burden and provide important …