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Related Concept Videos

Bootstrapping01:24

Bootstrapping

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The term "bootstrap" originated in the 19th century as a metaphor for self-improvement or achieving something independently, without external assistance. This concept extends to statistical bootstrapping, a self-contained method for estimating population parameters through resampling, even though it can be computationally intensive. Developed by the American statistician Dr. Bradley Efron in 1979, bootstrapping provides a robust way to perform inference when the original sample size is...
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Estimating Population Mean with Unknown Standard Deviation01:22

Estimating Population Mean with Unknown Standard Deviation

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In practice, we rarely know the population standard deviation. In the past, when the sample size was large, this did not present a problem to statisticians. They used the sample standard deviation s as an estimate for σ and proceeded as before to calculate a confidence interval with close enough results. However, statisticians ran into problems when the sample size was small. A small sample size caused inaccuracies in the confidence interval.
William S. Gosset (1876–1937) of the...
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Estimating Population Standard Deviation01:26

Estimating Population Standard Deviation

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When the population standard deviation is unknown and the sample size is large, the sample standard deviation s is commonly used as a point estimate of σ. However, it can sometimes under or overestimate the population standard deviation. To overcome this drawback, confidence intervals are determined to estimate population parameters and eliminate any calculation bias accurately. However, this only applies to random samples from normally distributed populations. Knowing the sample mean and...
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Estimating Population Mean with Known Standard Deviation01:16

Estimating Population Mean with Known Standard Deviation

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To construct a confidence interval for a single unknown population mean μ, where the population standard deviation is known, we need sample mean as an estimate for μ and we need the margin of error. Here, the margin of error (EBM) is called the error bound for a population mean (abbreviated EBM). The sample mean is the point estimate of the unknown population mean μ.
The confidence interval estimate will have the form as follows:
(point estimate - error bound, point estimate +...
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Distributions to Estimate Population Parameter01:26

Distributions to Estimate Population Parameter

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The accurate values of population parameters such as population proportion, population mean, and population standard deviation (or variance) are usually unknown. These are fixed values that can only be estimated from the data collected from the samples. The estimates of each of these parameters are sample proportion, the sample mean, and sample standard deviation (or variance). To obtain the values of these sample statistics, data are required that have particular distribution and central...
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Confidence Interval for Estimating Population Mean01:25

Confidence Interval for Estimating Population Mean

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A point estimate of the population mean is obtained from a single sample. Such a point estimate does not represent a population well because it needs to account for variability in the population. Single point estimate can also be biased despite the sample being selected randomly. Thus, a point estimate is often unreliable. A confidence interval is needed to reduce this unreliability.
A confidence interval for the mean is a range of values that provides an estimate of the population mean. As the...
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Multiply Robust Bootstrap Variance Estimation in the Presence of Singly Imputed Survey Data.

Sixia Chen1, David Haziza2, Zeinab Mashreghi3

  • 1Assistant Professor in the Department of Biostatistics and Epidemiology, The University of Oklahoma Health Sciences Center, Oklahoma City, OK 73126-0901, USA.

Journal of Survey Statistics and Methodology
|August 26, 2021
PubMed
Summary

This study introduces three pseudo-population bootstrap methods to accurately estimate variance in survey data after imputation. These methods address underestimation issues caused by single imputation, improving survey data analysis.

Keywords:
Bootstrap schemesItem nonresponseMultiply robust imputationRandom hot-deck imputationVariance estimation

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Area of Science:

  • Statistics
  • Survey Methodology
  • Computational Statistics

Background:

  • Single imputation is a common method for handling item nonresponse in surveys.
  • Treating imputed values as observed data can lead to underestimation of variance.
  • Accurate variance estimation is crucial for reliable statistical inference from survey data.

Purpose of the Study:

  • To propose novel bootstrap schemes for variance estimation after multiply robust imputation.
  • To develop methods that can handle large sampling fractions.
  • To provide variance estimators with the multiple robustness property.

Main Methods:

  • Development of three pseudo-population bootstrap schemes.
  • Application of multiply robust imputation procedures.
  • Simulation studies to evaluate performance.

Main Results:

  • The proposed bootstrap methods effectively estimate the variance of imputed estimators.
  • The methods demonstrate good performance in terms of relative bias and coverage probability.
  • The procedures are suitable for large sampling fractions.

Conclusions:

  • The proposed pseudo-population bootstrap schemes offer a robust approach to variance estimation in the presence of item nonresponse and imputation.
  • These methods improve the accuracy of statistical inference for population totals and quantiles.
  • The multiple robustness property enhances the reliability of the estimators.