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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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Uncertainty: Confidence Intervals00:54

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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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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.
Suppose a person calculates a confidence interval with a confidence coefficient of 0.95. In that case, they can...
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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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Bootstrapping01:24

Bootstrapping

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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...
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Regression Toward the Mean01:52

Regression Toward the Mean

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Regression toward the mean (“RTM”) is a phenomenon in which extremely high or low values—for example, and individual’s blood pressure at a particular moment—appear closer to a group’s average upon remeasuring. Although this statistical peculiarity is the result of random error and chance, it has been problematic across various medical, scientific, financial and psychological applications. In particular, RTM, if not taken into account, can interfere when...
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Related Experiment Video

Updated: Jan 20, 2026

Confidence Intervals
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Fast Bootstrap Confidence Intervals for Continuous Threshold Linear Regression.

Youyi Fong1

  • 1Vaccine and Infectious Disease Division, Fred Hutchinson Cancer Research Center, Department of Biostatistics, University of Washington, Seattle, WA 98109.

Journal of Computational and Graphical Statistics : a Joint Publication of American Statistical Association, Institute of Mathematical Statistics, Interface Foundation of North America
|August 30, 2019
PubMed
Summary
This summary is machine-generated.

Continuous threshold regression models are difficult to fit and yield accurate confidence intervals. This study introduces a fast grid search method using dynamic programming, significantly improving computational performance for threshold regression analysis.

Keywords:
change pointmodel-robustsegmented regression

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Area of Science:

  • Statistics
  • Econometrics
  • Machine Learning

Background:

  • Continuous threshold regression is a widely used nonlinear regression technique valued for its interpretability.
  • Widespread adoption is hindered by computational complexity and challenges in achieving accurate confidence interval coverage, especially under model misspecification.

Purpose of the Study:

  • To address the computational and inferential challenges in continuous threshold regression.
  • To develop a more efficient method for fitting threshold regression models and ensuring robust inference.

Main Methods:

  • Demonstrated the impracticality of ideal model-robust inference approaches for continuous threshold linear regression.
  • Developed a novel, fast grid search algorithm leveraging the dynamic programming principle.

Main Results:

  • The proposed dynamic programming-based grid search method offers a significant improvement in computational performance, orders of magnitude faster than existing approaches.
  • The new method facilitates more practical and efficient fitting of continuous threshold linear models.

Conclusions:

  • The developed fast grid search method overcomes key computational barriers in continuous threshold regression.
  • This advancement promotes wider adoption and more reliable application of threshold regression models in practice.