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Parametric prediction of finite population total under Informative sampling and nonignorable nonresponse

100%

Abdulhakeem E.

Statistics in Transition new series

2020

vol. 21

issue 1

13-35

In this paper, we combine two methodologies used in the model-based survey sampling, namely the prediction of the finite population total, named T, under informative sampling and full response, see Sverchkov and Pfeffermann (2004), and the prediction of T with a noninformative sampling design and the nonignorable nonresponse mechanism, see Eideh (2012). The former approach involves the dependence of the first order inclusion probabilities on the study variable, while the latter involves the dependence of the probability of nonresponse on unobserved or missing observations. The main aim of the paper is to consider how to account for the joint effects of informative sampling designs and notmissing- at-random response mechanism in statistical models for complex survey data. For this purpose, theoretically, we use the response distribution and relationships between the moments of the superpopoulation, the sample, sample-complement, response, and nonresponse distributions for the prediction of finite population totals, see Eideh (2016). The derived parametric predictors of T use the observation for the response set of the study variable or variable of interest, values of auxiliary variables and their population totals, sampling weights, and propensity scores. An interesting outcome of the T study is that most predictors known from model-based survey sampling can be derived as a special case from this general theory, see Chambers and Clark (2012).

On representativeness, informative sampling, nonignorable nonresponse, semiparametric prediction and calibration

88%

Eideh A.

Statistics in Transition new series

2023

vol. 24

issue 2

93-111

Informative sampling refers to a sampling design for which the sample selection probabilities depend on the values of the model outcome variable. In such cases the model holding for the sample data is different from the model holding for the population data. Similarly, nonignorable nonresponse refers to a nonresponse mechanism in which the response probability depends on the value of a missing outcome variable. For such a nonresponse mechanism the model holding for the response data is different from the model holding for the population data. In this paper, we study, within a modelling framework, the semi-parametric prediction of a finite population total by specifying the probability distribution of the response units under informative sampling and nonignorable nonresponse. This is the most general situation in surveys and other combinations of sampling informativeness and response mechanisms can be considered as special cases. Furthermore, based on the relationship between response distribution and population distribution, we introduce a new measure of the representativeness of a response set and a new test of nonignorable nonresponse and informative sampling, jointly. Finally, a calibration estimator is obtained when the sampling design is informative and the nonresponse mechanism is nonignorable.

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2 Statistics in Transition new series

1 Abdulhakeem E.

1 Eideh A.

1 2023

1 2020

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Parametric prediction of finite population total under Informative sampling and nonignorable nonresponse

On representativeness, informative sampling, nonignorable nonresponse, semiparametric prediction and calibration