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Variance01:15

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 The deviations show how spread out the data are about the mean. A positive deviation occurs when the data value exceeds the mean, whereas a negative deviation occurs when the data value is less than the mean. If the deviations are added, the sum is always zero. So one cannot simply add the deviations to get the data spread. By squaring the deviations, the numbers are made positive; thus, their sum will also be positive.
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Random or indeterminate errors originate from various uncontrollable variables, such as variations in environmental conditions, instrument imperfections, or the inherent variability of the phenomena being measured. Usually, these errors cannot be predicted, estimated, or characterized because their direction and magnitude often vary in magnitude and direction even during consecutive measurements. As a result, they are difficult to eliminate. However, the aggregate effect of these errors can be...
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How estimating nuisance parameters can reduce the variance (with consistent variance estimation).

Judith J Lok1

  • 1Department of Mathematics and Statistics, Boston University, Boston, Massachusetts, USA.

Statistics in Medicine
|July 31, 2024
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Summary
This summary is machine-generated.

This study introduces a novel sandwich estimator for variance estimation in complex statistical models. It demonstrates that estimating nuisance parameters can counter-intuitively reduce variance and improve confidence interval accuracy in causal inference.

Keywords:
confidence intervalsestimating equationsnuisance parametersvariance estimation

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Area of Science:

  • Statistics
  • Causal Inference
  • Econometrics

Background:

  • Estimating parameters of interest often involves nuisance parameters.
  • Standard methods like inverse probability weighting yield unbiased estimating equations.

Purpose of the Study:

  • To present a consistent sandwich estimator for variance in models with estimated nuisance parameters.
  • To provide four additional results for score equation settings, including causal inference, missing data, and measurement error.

Main Methods:

  • Development of a consistent sandwich estimator for variance.
  • Analysis of settings where nuisance parameters are estimated via score equations.
  • Application to observational data for confidence interval calculation.

Main Results:

  • Estimating nuisance parameters can lead to smaller asymptotic variance.
  • Ignoring nuisance parameter estimation results in a conservative variance estimator.
  • A consistent sandwich estimator for the nuisance parameter's variance is derived.
  • Asymptotic variance is independent of nuisance parameter estimation under efficiency conditions.

Conclusions:

  • The proposed methods offer improved variance estimation in complex statistical models.
  • Accurate variance estimation is crucial for reliable confidence intervals in causal inference and related fields.