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Related Concept Videos

Confidence Coefficient01:24

Confidence Coefficient

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The confidence coefficient is also known as the confidence level or degree of confidence. It is the percent expression for the probability, 1-α, that the confidence interval contains the true population parameter assuming that the confidence interval is obtained after sufficient unbiased sampling; for example, if the CL = 90%, then in 90 out of 100 samples the interval estimate will enclose the true population parameter. Here α is the area under the curve, distributed equally under...
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Confidence Intervals01:21

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An unbiased point estimate is often insufficient to predict a population estimate, such as population mean or population proportion. In this scenario, a confidence interval is used. A confidence interval is an estimate similar to a  sample proportion. However, unlike the point estimate which is a single value, the confidence interval  contains a range of values. These values have lower and upper limits, known as confidence limits, and can be designated as L1 and L2, respectively.
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Empirical Method to Interpret Standard Deviation01:09

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The empirical rule, also known as the three-sigma rule, allows a statistician to interpret the standard deviation in a normally distributed dataset. The rule states that 68% of the data lies within one standard deviation from the mean, 95% lies within two standard deviations from the mean, and 99.7% lies within three standard deviations from the mean. Additionally, this rule is also called the 68-95-99.7 rule.
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Interpretation of Confidence Intervals01:19

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A confidence interval is a better estimate of the population than a point estimate, as it uses a range of values from a sample instead of a single value.
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Uncertainty: Confidence Intervals00:54

Uncertainty: Confidence Intervals

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The confidence interval is the range of values around the mean that contains the true mean. It is expressed as a probability percentage. The interpretation of a 95% confidence interval, for instance, is that the statistician is 95% confident that the true mean falls within the interval. The upper and lower limits of this range are known as confidence limits. The confidence limits for the true mean are estimated from the sample's mean, the standard deviation, and the statistical factor...
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Theory of Attribution II: Kelley's Covariation Theory01:29

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Attribution theory plays a crucial role in social psychology, helping to explain how individuals interpret the causes of behavior. One prominent model within this field is Harold Kelley's covariation theory, which provides a systematic approach to determining whether internal traits or external circumstances drive a person's actions. The model posits that individuals rely on three key types of information—consensus, consistency, and distinctiveness—to make these judgments.Consensus:...
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Constrained empirical-likelihood confidence regions in nonignorable covariate-missing data problems.

Yanmei Xie1, Biao Zhang1

  • 1Department of Mathematics and Statistics, The University of Toledo, Toledo, Ohio.

Statistics in Medicine
|October 13, 2018
PubMed
Summary

This study introduces novel empirical-likelihood methods to address missing covariate data in regression analysis. These techniques improve confidence region accuracy for regression parameters, outperforming existing methods in simulations.

Keywords:
chi-squaredconstrained confidence regionempirical-likelihood ratio statisticmissing covariatesmissing not at randomregressionunbiased estimating function

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Area of Science:

  • Statistics
  • Biostatistics
  • Econometrics

Background:

  • Missing covariates are a significant challenge in medical, social, and economic research, potentially biasing regression analysis results.
  • Existing methods for handling missing covariate data often rely on strong assumptions or yield suboptimal performance.
  • Developing robust statistical methods is crucial for accurate parameter estimation in the presence of missing covariate information.

Purpose of the Study:

  • To develop and evaluate empirical-likelihood confidence regions for regression parameters in the presence of nonignorable missing covariate data.
  • To construct both unconstrained and constrained empirical-likelihood ratio statistics for robust parameter estimation.
  • To assess the finite-sample performance of the proposed methods compared to existing approaches.

Main Methods:

  • Developed a system of unbiased estimating equations by integrating a missingness probability model and a semiparametric conditional score model.
  • Introduced unconstrained and constrained empirical-likelihood ratio statistics based on the derived estimating equations.
  • Established the asymptotic distributions of the proposed empirical-likelihood ratio statistics.

Main Results:

  • The proposed empirical-likelihood methods demonstrated superior finite-sample performance in terms of coverage probability and interval length compared to competing methods.
  • The methods effectively construct confidence regions for regression parameters even with missing covariate data.
  • The approach was successfully applied to real-world data from the US National Health and Nutrition Examination Survey.

Conclusions:

  • The novel empirical-likelihood methods provide a powerful and accurate tool for regression analysis with missing covariate data.
  • These methods offer improved precision and reliability in estimating regression parameters, particularly in complex datasets.
  • The study highlights the utility of empirical likelihood in addressing challenging missing data problems across various research fields.