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Interpretation of Confidence Intervals01:19

Interpretation of Confidence Intervals

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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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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.
A...
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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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Critical Values01:31

Critical Values

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A critical value is a definite value obtained from a particular probability distribution at a predecided confidence level (or a predecided significance level) for a given population parameter. The critical value provides demarcation that separates the sample statistics that are likely to occur from the ones that are unlikely to occur based on the given probability distribution and the population parameter to be estimated. The critical value for normal distribution is obtained from the z...
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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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An Algorithm of Nonparametric Quantile Regression.

Journal of statistical theory and practice·2023
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A Method for Confidence Intervals of High Quantiles.

Mei Ling Huang1, Xiang Raney-Yan2

  • 1Department of Mathematics, Brock University, St. Catharines, ON L2S 3A1, Canada.

Entropy (Basel, Switzerland)
|January 7, 2021
PubMed
Summary
This summary is machine-generated.

This study introduces a novel geometric mean-based estimator for high quantiles in heavy-tailed distributions. The new method improves efficiency and reduces bias in confidence interval estimation for these challenging distributions.

Keywords:
Hill estimatorWeissman estimatorefficiencyextreme value distributionsgeneralized Pareto distributionmean square errorsorder statisticstail index

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Area of Science:

  • Statistics
  • Probability Theory
  • Data Analysis

Background:

  • Heavy-tailed distributions present theoretical challenges due to infinite moments.
  • Existing methods for high quantile confidence intervals (CIs) suffer from bias issues.

Purpose of the Study:

  • To propose a new, efficient, and unbiased estimator for high quantiles of heavy-tailed distributions.
  • To develop a computational algorithm for estimating confidence intervals of high quantiles.

Main Methods:

  • Development of a novel high quantile estimator utilizing the geometric mean.
  • Theoretical analysis of asymptotic properties and bias reduction.
  • Monte Carlo simulations for empirical validation.

Main Results:

  • The proposed geometric mean-based estimator demonstrates good asymptotic properties.
  • The new estimator effectively reduces bias compared to existing methods.
  • Computational algorithm for CIs is provided and validated.

Conclusions:

  • The novel estimator offers an improved approach for high quantile estimation in heavy-tailed distributions.
  • The method addresses theoretical difficulties and practical bias issues.
  • Demonstrated applicability through simulations and real-world examples.