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Related Concept Videos

Confidence Intervals01:21

Confidence Intervals

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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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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.
Confidence intervals have confidence coefficients that are crucial for their interpretation. The most common confidence coefficients are 0.90, 0.95, and 0.99, which can be written as percentages–90%, 95%, and 99%, respectively.
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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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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.
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Prediction Intervals

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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. 
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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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Inverse set estimation and inversion of simultaneous confidence intervals.

Junting Ren1, Fabian J E Telschow2, Armin Schwartzman1,3

  • 1Division of Biostatistics, University of California San Diego, La Jolla, CA, USA.

Journal of the Royal Statistical Society. Series C, Applied Statistics
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PubMed
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This study introduces a new method for estimating function domains in climatology and medicine, offering robust protection against errors in data analysis. The approach provides reliable confidence sets for complex datasets.

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bootstrapinverse setnonparametricsimultaneous confidence bands

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Area of Science:

  • Statistics
  • Climatology
  • Medicine

Background:

  • Risk assessment in climatology (North American temperature change) and medicine (statin use, COVID-19 impact) requires accurate domain estimation.
  • Current methods for estimating function domains with specific image subsets are limited by strict assumptions.

Purpose of the Study:

  • To generalize the estimation of function domains for sets whose image equals a predefined subset of the real line.
  • To provide protection against inflated Type I error in exploratory data analysis for both dense and nondense domains.

Main Methods:

  • Developed a method to construct simultaneous confidence sets (upper, lower, or interval) for function domains.
  • Utilized the inversion of simultaneous confidence intervals for nonasymptotic confidence.
  • Provided a nonparametric bootstrap algorithm and accompanying code for practical application.

Main Results:

  • Successfully generalized domain estimation to dense and nondense domains.
  • Demonstrated protection against inflated Type I error, enhancing reliability in exploratory data analysis.
  • Established a method for constructing multiple simultaneous confidence sets with desired confidence levels.

Conclusions:

  • The proposed method offers a more flexible and robust approach to domain estimation compared to existing techniques.
  • This advancement is applicable to critical areas like climate change risk assessment and medical patient data analysis.
  • The provided algorithm and code facilitate the implementation of these advanced statistical methods.