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Related Concept Videos

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...
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...
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...
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...
Prediction Intervals01:03

Prediction Intervals

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. 
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...

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Published on: August 1, 2017

Adaptive Confidence Intervals for the Test Error in Classification.

Eric B Laber1, Susan A Murphy

  • 1Department of Statistics at the University of Michigan, Ann Arbor, MI, 48109.

Journal of the American Statistical Association
|November 5, 2011
PubMed
Summary
This summary is machine-generated.

Estimating classifier test error is challenging. This study introduces a novel confidence interval method that directly bounds test error, ensuring reliable coverage across various classifiers and sample sizes.

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Area of Science:

  • Machine Learning
  • Statistical Inference
  • Computer Science

Background:

  • Classifier performance is commonly measured by estimated test error.
  • Accurate point and interval estimation of test error remains a significant challenge.
  • Existing confidence intervals often fail to provide reliable coverage due to issues with point estimation.

Purpose of the Study:

  • To develop a robust method for constructing confidence intervals for classifier test error.
  • To address the limitations of traditional interval estimators that rely on point estimates.
  • To ensure reliable coverage properties for classifier performance evaluation.

Main Methods:

  • Direct construction of confidence intervals using smooth, data-dependent bounds on test error.
  • Theoretical analysis for linear classifiers, proving consistency and adaptability.
  • Empirical validation across diverse classification algorithms and sample sizes.

Main Results:

  • The proposed confidence interval method adapts to the non-smoothness of test error.
  • The method is consistent under fixed and local alternatives for linear classifiers.
  • Nominal coverage is achieved across various test problems, classifiers, and sample sizes.

Conclusions:

  • The novel approach overcomes the difficulties associated with point estimation of test error.
  • This method offers a more reliable way to assess classifier performance using confidence intervals.
  • The technique is broadly applicable to different classification algorithms and data scenarios.