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Related Concept Videos

Bootstrapping01:24

Bootstrapping

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 small or...
Estimating Population Mean with Unknown Standard Deviation01:22

Estimating Population Mean with Unknown Standard Deviation

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 Guinness...
Estimating Population Mean with Known Standard Deviation01:16

Estimating Population Mean with Known Standard Deviation

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 + error bound)
The...
Estimating Population Standard Deviation01:26

Estimating Population Standard Deviation

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...
Prediction Intervals01:03

Prediction Intervals

The interval estimate of any variable is known as the prediction interval. It helps decide if a point estimate is dependable.
However, the point estimate is most likely not the exact value of the population parameter, but close to it. After calculating point estimates, we construct interval estimates, called confidence intervals or prediction intervals. This prediction interval comprises a range of values unlike the point estimate and is a better predictor of the observed sample value, y. 
The...
Distributions to Estimate Population Parameter01:26

Distributions to Estimate Population Parameter

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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Related Experiment Videos

Using an Approximate Bayesian Bootstrap to Multiply Impute Nonignorable Missing Data.

Juned Siddique1, Thomas R Belin

  • 1University of Chicago, Department of Health Studies, Chicago, IL 60637, USA.

Computational Statistics & Data Analysis
|December 18, 2009
PubMed
Summary
This summary is machine-generated.

This study introduces a new Approximate Bayesian Bootstrap (ABB) method for handling complex missing data. The novel approach effectively imputes nonignorable missing data, ensuring accurate uncertainty and reliable inferences in statistical analyses.

Related Experiment Videos

Area of Science:

  • Statistics
  • Biostatistics
  • Data Science

Background:

  • Approximate Bayesian Bootstrap (ABB) is useful for data imputation with uncertainty.
  • Existing ABB methods struggle with nonignorable missing data, where missingness depends on unobserved values.

Purpose of the Study:

  • To present a strategy for using ABB to multiply impute nonignorable missing data.
  • To enable valid inferences and sensitivity analyses when missing data mechanisms are not ignorable.

Main Methods:

  • A novel strategy for Approximate Bayesian Bootstrap (ABB) is outlined for multiply imputing nonignorable missing data.
  • The method involves using a distinct ABB type for each imputed dataset to manage uncertainty.

Main Results:

  • The proposed ABB strategy successfully imputes nonignorable missing data.
  • The method demonstrates appropriate uncertainty accounting and provides nominal coverage in both a depression trial and a simulation study.

Conclusions:

  • The developed ABB method effectively addresses nonignorable missing data.
  • This approach enhances the reliability of statistical inferences and sensitivity analyses in the presence of complex missing data mechanisms.