Remembering Professor Dalho Kim: A Memorial session

We have very limited information from a probability sample (ps) and we want to make inference about small areas using a much larger non-probability sample (nps). In our procedure we use the survey weights from the survey sample to estimate domain sizes, where the domains are formed based on distinct covariates, possibly discretized. The propensity scores that are currently used cannot be interpreted as selection probabilities because the selection probabilities should be obtained for the entire population, calibrated to a sample size. We discuss both the ignorable case and the non-ignorable case (study variable is not observed for the probability sample, and they are not used in our procedure). The models for the study variable are used at the domain level. We provide Bayesian predictive inference for the finite population means of the small areas, which are not part of the models, but they are tracked. The methodology is illustrated using an example on body mass index.  

This paper introduces a novel semiparametric model-assisted estimation method that integrates data from both probability and nonprobability samples, thereby facilitating robust and efficient inferences regarding finite population parameters. To mitigate selection bias, whether ignorable or nonignorable, associated with the nonprobability sample, we propose a flexible semiparametric propensity score model that extends beyond the missing at random assumption. Our approach employs a pseudo-profile-likelihood method to estimate the propensity score model. Subsequently, a difference estimator is constructed utilizing the probability sample as a foundation, where the proxy values of the study variable for the finite population are derived from the nonprobability sample using the estimated propensity score model. We present the asymptotic properties of the proposed estimators and provide formulae for variance estimation. Through a series of simulations, we validate our proposed estimation procedure and demonstrate its robustness and superiority over some existing estimators.
 

Incorporating the auxiliary information into the survey estimation is a fundamental problem in survey sampling. Calibration weighting is a popular tool for incorporating the auxiliary information. The calibration weighting method of Deville and Sarndal (1992) uses a distance measure between the design weights
and the final weights to solve the optimization problem with calibration constraints.
In this paper, we propose a new framework using generalized entropy as the objective
function for optimization. Design weights are used in the constraints, rather than in the objective function, to achieve design consistency. The new calibration framework is attractive as it is general and can produce more efficient calibration weights than the classical calibration weights. Furthermore, we identify the optimal choice of the generalized entropy function that achieves the minimum variance among the different choices of the generalized entropy function under the same constraints. Results from a limited simulation study are also presented.  

The analysis of complex networks has become increasingly popular in many scientific fields, with network topology measures providing insights into the relationships between network elements. The Betti curve, a mathematical tool derived from the persistent homology of a network, is used to represent the dynamic topological structure of a complex, weighted network. However, previous studies have primarily focused on the shape of the Betti curve to investigate differences in the dynamic topology of complex networks, without considering the impact of edge weight strength. In this study, we show that the shape of the Betti curve is influenced by both the network organization and the weight strength of the edges. We also introduce a novel Betti curve representation that can detect topological differences in networks without being affected by weight strength differences. The proposed topological noise curve provides a more accurate comparison of the topological structures of different weighted networks.