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Related Concept Videos

Interpretation of Confidence Intervals01:19

Interpretation of Confidence Intervals

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...
Uncertainty: Confidence Intervals00:54

Uncertainty: Confidence Intervals

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 't,' or...
Confidence Intervals01:21

Confidence Intervals

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 confidence...
Confidence Coefficient01:24

Confidence Coefficient

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 both the...
Accuracy and Errors in Hypothesis Testing01:13

Accuracy and Errors in Hypothesis Testing

Hypothesis testing is a fundamental statistical tool that begins with the assumption that the null hypothesis H0 is true. During this process, two types of errors can occur: Type I and Type II. A Type I error refers to the incorrect rejection of a true null hypothesis, while a Type II error involves the failure to reject a false null hypothesis.
In hypothesis testing, the probability of making a Type I error, denoted as α, is commonly set at 0.05. This significance level indicates a 5% chance...
Confidence Interval for Estimating Population Mean01:25

Confidence Interval for Estimating Population Mean

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 R-Based Landscape Validation of a Competing Risk Model
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An R-Based Landscape Validation of a Competing Risk Model

Published on: September 16, 2022

Comment on "Adaptive Confidence Intervals for the Test Error in Classification"

Yair Goldberg1, Michael R Kosorok

  • 1postdoctoral scholar in the Department of Biostatistics, University of North Carolina at Chapel Hill, Chapel Hill, NC 27599 ( ygoldber@bios.unc.edu ).

Journal of the American Statistical Association
|June 7, 2013
PubMed
Summary
This summary is machine-generated.

This study introduces adaptive classifiers with improved performance. These new methods demonstrate an "oracle property," leading to reduced variance and test error compared to existing classifiers.

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Area of Science:

  • Statistical Learning Theory
  • Machine Learning

Background:

  • Non-regular statistical frameworks present challenges for classifier performance.
  • Existing classifiers may exhibit suboptimal variance and test error.

Purpose of the Study:

  • To propose a novel family of adaptive classifiers inspired by non-regular frameworks.
  • To analyze the asymptotic properties and performance of these new classifiers.
  • To demonstrate the consistency of confidence intervals for test error.

Main Methods:

  • Development of adaptive classifiers based on the non-regular framework.
  • Asymptotic analysis of classifier properties.
  • Application of normal approximation and centered percentile bootstrap for confidence intervals.

Main Results:

  • The proposed adaptive classifiers exhibit an
  • oracle property
  • under the non-regular framework.
  • Demonstrated smaller asymptotic variance and asymptotic test error variance compared to original classifiers.
  • Established consistency of confidence intervals for test error using both normal approximation and bootstrap methods.

Conclusions:

  • Adaptive classifiers offer significant improvements in statistical learning.
  • The proposed methods provide a robust approach for handling non-regular data structures.
  • Confidence intervals for test error are reliable for the new adaptive classifiers.