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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...
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 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...
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...
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...

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A Machine Learning Approach to Design an Efficient Selective Screening of Mild Cognitive Impairment
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Published on: January 11, 2020

A Confidence Region Approach to Tuning for Variable Selection.

Funda Gunes1, Howard D Bondell

  • 1Department of Statistics, North Carolina State University.

Journal of Computational and Graphical Statistics : a Joint Publication of American Statistical Association, Institute of Mathematical Statistics, Interface Foundation of North America
|February 15, 2013
PubMed
Summary
This summary is machine-generated.

We introduce a new method for tuning penalized regression variable selection using confidence regions. This approach is more intuitive and often outperforms traditional methods like AIC, BIC, and cross-validation (CV).

Keywords:
Adaptive LASSOConfidence regionPenalized regressionTuning parameterVariable selection

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Area of Science:

  • Statistics
  • Machine Learning
  • Data Science

Background:

  • Penalized regression methods are widely used for variable selection in statistical modeling.
  • Current tuning methods like AIC, BIC, and cross-validation (CV) can be complex and their performance varies.
  • Understanding and improving the tuning process is crucial for reliable model selection.

Purpose of the Study:

  • To develop an intuitive and effective approach for tuning penalized regression variable selection methods.
  • To compare the proposed method with existing tuning techniques.
  • To establish theoretical guarantees for the new tuning approach.

Main Methods:

  • Proposing a novel tuning approach based on confidence regions.
  • Calculating the sparsest estimator within a specified confidence region.
  • Analyzing the performance against AIC, BIC, and CV across various scenarios.
  • Proving theoretical properties such as selection consistency and oracle property.

Main Results:

  • The confidence region tuning method is more intuitive and easier for practitioners to understand.
  • This approach frequently demonstrates superior performance compared to AIC, BIC, and CV.
  • Tuning with confidence levels converging to one achieves asymptotic selection consistency.
  • A two-stage procedure yields an oracle property, selecting the best model consistently.

Conclusions:

  • Confidence region-based tuning offers a robust and interpretable alternative for penalized regression.
  • The method provides strong theoretical backing, including selection consistency and oracle properties.
  • This approach simplifies model selection and enhances the reliability of penalized regression techniques.