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Prediction Intervals

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...

Confidence Intervals

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 Intervals

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 Intervals

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...

Residuals and Least-Squares Property

Residuals and Least-Squares Property

The vertical distance between the actual value of y and the estimated value of y. In other words, it measures the vertical distance between the actual data point and the predicted point on the line
If the observed data point lies above the line, the residual is positive, and the line underestimates the actual data value for y. If the observed data point lies below the line, the residual is negative, and the line overestimates the actual data value for y.
The process of fitting the best-fit...

Confidence Interval for Estimating Population Mean

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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Related Experiment Videos

Approximate confidence and prediction intervals for least squares support vector regression.

Kris De Brabanter¹, Jos De Brabanter, Johan A K Suykens

¹Department of Electrical Engineering, Research Division SCD, Katholieke Universiteit Leuven, Leuven 3001, Belgium. kris.debrabanter@esat.kuleuven.be

IEEE Transactions on Neural Networks

|November 5, 2010

Summary

New bias-corrected confidence intervals for least squares support vector machines (LS-SVM) are proposed. This method offers similar accuracy to bootstrap techniques but with significantly reduced computational expense for LS-SVM analysis.

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Area of Science:

Machine Learning
Statistical Modeling
Computational Statistics

Background:

Least Squares Support Vector Machines (LS-SVM) are powerful tools for classification and regression.
Accurate confidence and prediction intervals are crucial for assessing the reliability of LS-SVM models.
Existing methods for interval estimation can be computationally intensive or lack robustness.

Purpose of the Study:

To propose novel bias-corrected approximate confidence and prediction intervals for LS-SVM.
To develop a computationally efficient method for bias estimation without higher-order derivatives.
To provide robust variance estimation for both homoscedastic and heteroscedastic data.

Main Methods:

Formulation of a simple bias determination method.
Development of a variance estimator applicable to homoscedastic and heteroscedastic scenarios.
Implementation of Šidák correction and upcrossing theory-based corrections for simultaneous intervals.

Main Results:

The proposed method generates bias-corrected pointwise and simultaneous confidence and prediction intervals.
The variance estimator performs effectively across different data variance structures.
Simulations demonstrate that the new intervals are comparable in accuracy to bootstrap methods.

Conclusions:

The proposed bias-corrected interval estimation method for LS-SVM is effective and computationally efficient.
This approach offers a viable alternative to computationally expensive bootstrap methods.
The developed techniques provide reliable interval estimation for LS-SVM in various statistical settings.