Integrating probability and nonprobability survey samples is an important problem in modern survey sampling. Nonprobability samples often contain rich outcome information but may lack population representativeness, whereas probability samples provide design-based auxiliary information but may not contain the study variable. We propose a deep neural network (DNN)-assisted doubly robust framework for estimating the finite population mean from these two data sources. The proposed method models the logit sampling score for the nonprobability sample as an unknown nonparametric function and estimates it by maximizing a pseudo-likelihood that combines information from the nonprobability sample and a reference probability sample. The DNN parameters are optimized using the ADAM algorithm. The resulting DNN-estimated sampling scores are incorporated into a DNN-assisted inverse-probability weighted estimator and a deep doubly robust estimator. We establish consistency and convergence rates under regularity conditions and evaluate the finite-sample performance of the proposed estimators through simulation studies and an empirical application using Pew Research Center and Behavioral Risk Factor Surveillance System data. The results suggest that the proposed estimators can improve robustness to parametric propensity-score misspecification, especially when the true selection mechanism is nonlinear.

While synthetic data hold great promise for privacy protection, their statistical analysis poses significant challenges that necessitate innovative solutions.

Uncertainty is introduced in optimized DNNs through stochastic algorithms, forming specific distributions.

While synthetic data hold great promise for privacy protection, their statistical analysis poses significant challenges that necessitate innovative solutions.

Prediction-powered inference (PPI) is a recent framework for valid statistical inference with partially labeled data, combining model-based predictions on a large unlabeled set with bias correction from a smaller labeled subset. We show that PPI can be extended to handle informative labeling by replacing its unweighted bias-correction term with an inverse probability weighted (IPW) version, using the classical Horvitz--Thompson or Hájek forms. This connection unites design-based survey sampling ideas with modern prediction-assisted inference, yielding estimators that remain valid when labeling probabilities vary across units. We consider the common setting where the inclusion probabilities are not known but estimated from a correctly specified model. In simulations, the performance of IPW-adjusted PPI with estimated propensities closely matches the known-probability case, retaining both nominal coverage and the variance-reduction benefits of PPI.

While synthetic data hold great promise for privacy protection, their statistical analysis poses significant challenges that necessitate innovative solutions. The use of deep generative models (DGMs) for synthetic data generation is known to induce considerable bias and imprecision into synthetic data analyses, compromising their inferential utility as opposed to original data analyses. This bias and uncertainty can be substantial enough to impede statistical convergence rates, even in seemingly straightforward analyses like mean calculation. The standard errors of such estimators then exhibit slower shrinkage with sample size than the typical 1 over root-$n$ rate. This complicates fundamental calculations like p-values and confidence intervals, with no straightforward remedy currently available. In response to these challenges, we propose a new strategy that targets synthetic data created by DGMs for specific data analyses. Drawing insights from debiased and targeted machine learning, our approach accounts for biases, enhances convergence rates, and facilitates the calculation of estimators with easily approximated large sample variances. We exemplify our proposal through a simulation study on toy data and two case studies on real-world data, highlighting the importance of tailoring DGMs for targeted data analysis. This debiasing strategy contributes to advancing the reliability and applicability of synthetic data in statistical inference.

The method in which we select samples to learn more about characteristics in a given population is called hypothesis testing. Hypothesis testing is really a systematic way to test claims or ideas about a group or population. To illustrate, suppose we read an article stating that children in the United States watch an average of 3 hours of TV per week. To test whether this claim is true, we record the time (in hours) that a group of 20 American children (the sample), among all children in the United States (the population), watch TV. The mean we measure for these 20 children is a sample mean. We can then compare the sample mean we select to the population mean stated in the article. Hypothesis testing or significance testing is a method for testing a claim or hypothesis about a parameter in a population, using data measured in a sample. In this method, we test some hypothesis by determining the likelihood that a sample statistic could have been selected, if the hypothesis regarding the population parameter were true. To begin, we identify a hypothesis or claim that we feel should be tested. For example, we might want to test the claim that the mean number of hours that children in the United States watch TV is 3 hours.

Engineers may have a hard time understanding the research papers in data science, machine learning, or deep learning. The real issue is not because it is hard. It was taught in different domains over many years in different lingos. In this series, let's give it a try to make it more approachable. We will divide the fundamental topics on statistics into two articles.

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