Assessing the Impact of Sampling Methods on Estimation Precision in Finite Population Inference under Different Missing Data Mechanisms: A Comparative Study Using Bootstrap and Jackknife Resampling Techniques

Project Abstract

This study investigates how sampling methods influence estimation precision in finite population inference when data are subject to different missing data mechanisms, comparing bootstrap and jackknife resampling techniques as evaluative tools. We frame the problem within a finite population context where unit-level characteristics are partially observed, introducing missingness patterns that may be Missing Completely at Random (MCAR), Missing at Random (MAR), or Missing Not at Random (MNAR). Our objective is to quantify the impact of sampling design (e.g., simple random sampling, stratified sampling, cluster sampling) on estimator bias, variance, and mean squared error under varying missing data scenarios, and to assess how bootstrap and jackknife procedures perform in bias correction, variance estimation, and confidence interval construction. We develop a rigorous theoretical framework linking sampling design properties, missing data mechanisms, and resampling-based inference. The study derives analytical expressions for the sampling and imputation-induced variability of popular finite-population estimators, including Horvitz-Thompson-type estimators and model-assisted estimators, under complete-case and imputation-augmented schemes. We then implement extensive simulation experiments that mirror realistic survey settings with varying population sizes, sampling fractions, stratification schemes, and missingness intensities. Scenarios are designed to isolate the effects of design variance versus nonresponse variance, enabling a clear comparison of bootstrap methods (e.g., standard bootstrap, stratified bootstrap, and weighted bootstrap) and jackknife variants (e.g., delete-a-group, delete-one, and bootstrap-t adjustments) in terms of coverage probability, interval length, and computational efficiency. Key findings reveal nuanced interactions between sampling design and missing data mechanisms. When MCAR or MAR prevails, resampling-based estimators generally provide reliable variance estimates and confidence intervals, with stratified and cluster-aware bootstrap enhancing coverage in stratified and multi-stage designs. Under MNAR, standard resampling methods exhibit noticeable under-coverage unless coupled with appropriate modeling of the missing data mechanism or auxiliary variables, highlighting the necessity of joint modeling or sensitivity analyses. Jackknife methods tend to be more robust to complex survey designs in small samples but can underperform in heavy-tailed or highly imbalanced strata, whereas bootstrap methods demonstrate greater flexibility across diverse design structures, at the cost of higher computational demand. The study also evaluates diagnostic tools to assess the appropriateness of resampling-based inference in finite populations with nonignorable missingness, including influence diagnostics, bootstrap-based bias checks, and convergence assessments for iterative imputation procedures. Practical recommendations are formulated for survey practitioners and statisticians selecting resampling techniques aligned with the missing data mechanism, incorporating design weights, employing stratification-aware resampling, and performing sensitivity analyses to MNAR assumptions. The contribution extends methodological guidance for finite population inference under incomplete data, offering concrete protocols for implementing bootstrap and jackknife procedures in complex survey settings and illustrating their performance through replicable computational experiments.

Project Overview

What This Project Is About

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This project explores how different sampling methods affect how precisely we can estimate facts about a whole group (the finite population) when some data is missing. It compares bootstrap and jackknife resampling techniques to see which method gives more reliable estimates under various missing data scenarios.

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The Problem It Addresses

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Researchers often rely on samples to learn about a larger group, but missing data can bias results and reduce accuracy. There is a need to understand which sampling choices minimize error and how resampling tools help measure uncertainty in those cases.

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Objectives of the Project

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1. Explain how different sampling methods work in simple terms.
2. Show how missing data affects estimation accuracy.
3. Compare bootstrap and jackknife approaches on sample data with missing values.
4. Provide practical guidelines for choosing methods in real surveys.

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What You Will Do Step by Step

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1. Review basic concepts of sampling, estimation, and missing data in plain language.
2. Set up simulated datasets with known characteristics and controlled missingness.
3. Apply bootstrap and jackknife resampling to estimate accuracy and uncertainty.
4. Analyze results to identify which method performs better under different conditions.
5. Summarize findings into practical recommendations for researchers.

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Expected Outcome

Clear, user-friendly guidance on which resampling method to use in common survey situations, with explanations of when missing data might change the best choice and how to interpret resampling results.