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Aditi Sen

Publications and source records attributed to Aditi Sen.

5 recordsLinked to original sources
arXiv2025

Reconciliation of Bayes and empirical Bayes interval estimation with application to small area estimation

Multi-level normal hierarchical models, also interpreted as mixed effects models, play an important role in developing statistical theory in multi-parameter estimation for a wide range of applications, including small area estimation. In this article, we propose a novel reconciliation framework of the empirical Bayes (EB) and hierarchical Bayes approaches for interval estimation of random effects under a two-level normal model. Our framework shows that a second-order efficient empirical Bayes confidence interval, with EB coverage error of order $O(m^{-3/2})$, $m$ being the number of areas in the area-level model, can also be viewed as a credible interval whose expected posterior coverage is close to the nominal level, provided a carefully chosen prior, referred to as a "matching prior", is placed on the hyperparameters. While existing literature has examined matching priors that reconcile frequentist and Bayesian inference in various settings, this paper is the first to study matching priors with the goal of interval estimation of random effects in a two-level model. We obtain a matching prior on the variance component that achieves a proper posterior under mild regularity conditions. The theoretical results in the paper are corroborated through a Monte Carlo simulation study and real data analysis.

math.ST↗
arXiv2024

Improving measurement error and representativeness in nonprobability surveys

In the age of big data, nonprobability surveys are becoming increasingly abundant. Data integration techniques involving both probability and nonprobability surveys are being extensively used for providing improved estimates for finite population estimation. While much of the existing research has focused on mitigating selection bias in nonprobability surveys, the issue of measurement error within these surveys remains relatively unexplored. Statistical methods devised with the purpose of reducing selection bias are appropriate for reliable estimation, only under the assumption of accuracy of survey responses. Motivated by a recent case study of Kennedy, Mercer, and Lau (2024), our research addresses bias from both measurement and sampling errors in nonprobability surveys. In this article, we propose a new data integration method that uses multiple probability and nonprobability surveys and leverages machine learning models to construct a composite estimator. The proposed composite estimator integrates probability and nonprobability surveys, when both contain response variables of interest. We analyze the performance of this estimator in comparison to an existing composite estimator in literature, analytically as well as empirically, using multiple survey data from Kennedy et al. (2024). Finally, we identify conditions under which the proposed estimator outperforms estimators based solely on probability surveys.

stat.AP↗
arXiv2023

Estimation of finite population proportions for small areas -- a statistical data integration approach

Empirical best prediction (EBP) is a well-known method for producing reliable proportion estimates when the primary data source provides only small or no sample from finite populations. There are potential challenges in implementing existing EBP methodology such as limited auxiliary variables in the frame (not adequate for building a reasonable working predictive model) or unable to accurately link the sample to the finite population frame due to absence of identifiers. In this paper, we propose a new data linkage approach where the finite population frame is replaced by a big probability sample, having a large set of auxiliary variables but not the outcome binary variable of interest. We fit an assumed model on the small probability sample and then impute the outcome variable for all units of the big sample to obtain standard weighted proportions. We develop a new adjusted maximum likelihood (ML) method so that the estimate of model variance doesn't fall on the boundary, which is otherwise encountered in commonly used ML method. We also propose an estimator of the mean squared prediction error using a parametric bootstrap method and address computational issues by developing an efficient Expectation Maximization algorithm. The proposed methodology is illustrated in the context of election projection for small areas.

stat.ME↗
arXiv2021

Estimation of mask effectiveness perception for small domains using multiple data sources

All pandemics are local; so learning about the impacts of pandemics on public health and related societal issues at granular levels is of great interest. COVID-19 is affecting everyone in the globe and mask wearing is one of the few precautions against it. To quantify people's perception of mask effectiveness and to prevent the spread of COVID-19 for small areas, we use Understanding America Study's (UAS) survey data on COVID-19 as our primary data source. Our data analysis shows that direct survey-weighted estimates for small areas could be highly unreliable. In this paper we develop a synthetic estimation method to estimate proportions of mask effectiveness for small areas using a logistic model that combines information from multiple data sources. We select our working model using an extensive data analysis facilitated by a new variable selection criterion for survey data and benchmarking ratios. We propose a Jackknife method to estimate variance of our proposed estimator. From our data analysis. it is evident that our proposed synthetic method outperforms direct survey-weighted estimator with respect to commonly used evaluation measures.

stat.AP↗