Jove
Visualize
Contact Us
JoVE
x logofacebook logolinkedin logoyoutube logo
ABOUT JoVE
OverviewLeadershipBlogJoVE Help Center
AUTHORS
Publishing ProcessEditorial BoardScope & PoliciesPeer ReviewFAQSubmit
LIBRARIANS
TestimonialsSubscriptionsAccessResourcesLibrary Advisory BoardFAQ
RESEARCH
JoVE JournalMethods CollectionsJoVE Encyclopedia of ExperimentsArchive
EDUCATION
JoVE CoreJoVE BusinessJoVE Science EducationJoVE Lab ManualFaculty Resource CenterFaculty Site
Terms & Conditions of Use
Privacy Policy
Policies

Related Concept Videos

Calibration Curves: Linear Least Squares01:20

Calibration Curves: Linear Least Squares

A calibration curve is a plot of the instrument's response against a series of known concentrations of a substance. This curve is used to set the instrument response levels, using the substance and its concentrations as standards. Alternatively, or additionally, an equation is fitted to the calibration curve plot and subsequently used to calculate the unknown concentrations of other samples reliably.
For data that follow a straight line, the standard method for fitting is the linear...
Mean Absolute Deviation01:13

Mean Absolute Deviation

The mean absolute deviation is also a measure of the variability of data in a sample. It is the absolute value of the average difference between the data values and the mean.
Let us consider a dataset containing the number of unsold cupcakes in five shops: 10, 15, 8, 7, and 10. Initially, calculate the sample mean. Then calculate the deviation, or the difference, between each data value and the mean. Next, the absolute values of these deviations are added and divided by the sample size to...
Linear Approximation in Frequency Domain01:26

Linear Approximation in Frequency Domain

Linear systems are characterized by two main properties: superposition and homogeneity. Superposition allows the response to multiple inputs to be the sum of the responses to each individual input. Homogeneity ensures that scaling an input by a scalar results in the response being scaled by the same scalar.
In contrast, nonlinear systems do not inherently possess these properties. However, for small deviations around an operating point, a nonlinear system can often be approximated as linear.
Linear Approximation in Time Domain01:21

Linear Approximation in Time Domain

Nonlinear systems often require sophisticated approaches for accurate modeling and analysis, with state-space representation being particularly effective. This method is especially useful for systems where variables and parameters vary with time or operating conditions, such as in a simple pendulum or a translational mechanical system with nonlinear springs.
For a simple pendulum with a mass evenly distributed along its length and the center of mass located at half the pendulum's length, the...
Maximizing the Directional Derivative01:25

Maximizing the Directional Derivative

The directional derivative is a central concept in multivariable calculus that describes how a function changes at a given point when moving in a specified direction. This direction is represented by a unit vector, ensuring that only the orientation influences the rate of change. By varying the direction, different rates of change can be observed, demonstrating that the directional derivative depends strongly on the chosen direction.The directional derivative is computed using the gradient...
Derivatives of Inverse Trigonometric Functions01:30

Derivatives of Inverse Trigonometric Functions

A ship tracking an approaching aircraft relies on geometric measurements to find out the aircraft’s position relative to the observer. By measuring the slant distance to the aircraft and the angle of elevation, the horizontal and vertical components of the distance can be obtained using trigonometric relationships. This geometric approach provides a basis for analyzing how the observed angle changes as the aircraft moves closer to the ship.To examine the mathematical behavior of the angle of...

You might also read

Related Articles

Articles linked to this work by shared authors, journal, and citation graph.

Sort by
Same author

Delphinidin targets voltage-dependent anion channel 1 to inhibit ferroptosis and protect against retinal photochemical damage.

Phytomedicine : international journal of phytotherapy and phytopharmacology·2026
Same author

Genome-wide analysis of the <i>GID</i> gene family in soybean and analysis of expression under gibberellin treatment.

Frontiers in plant science·2026
Same author

Decentralized EM algorithm for Gaussian mixtures under data heterogeneity and partial labeling.

Biometrics·2026
Same author

Multiscale multimodal graph convolutional networks for identifying essential tremor and dystonic tremor.

Neurobiology of disease·2026
Same author

Quantitative venous outflow profiles based on four-dimensional computed tomography angiography are associated with tissue level collaterals and clinical outcomes of acute ischemic stroke patients.

Quantitative imaging in medicine and surgery·2026
Same author

Venous outflow time profiles: promising imaging biomarkers for futile recanalization in acute ischemic stroke due to large vessel occlusion.

Frontiers in neurology·2026
Same journal

Individualized dynamic latent factor model for multi-resolutional data with application to mobile health.

Biometrika·2026
Same journal

Functional principal component analysis forsparse censored data.

Biometrika·2026
Same journal

Finding distributions that differ, with false discovery rate control.

Biometrika·2026
Same journal

Sequential Gibbs posteriors with applications to principal component analysis.

Biometrika·2026
Same journal

Comparing causal parameters with many treatments and positivity violations.

Biometrika·2026
Same journal

Leveraging External Data for Testing Experimental Therapies with Biomarker Interactions in Randomized Clinical Trials.

Biometrika·2026
See all related articles

Related Experiment Video

Updated: Jun 24, 2026

Experimental and Data Analysis Workflow for Soft Matter Nanoindentation
13:04

Experimental and Data Analysis Workflow for Soft Matter Nanoindentation

Published on: January 18, 2022

Tuning parameter selectors for the smoothly clipped absolute deviation method.

Hansheng Wang1, Runze Li, Chih-Ling Tsai

  • 1Guanghua School of Management, Peking University, Beijing, China, 100871 hansheng@gsm.pku.edu.cn.

Biometrika
|April 4, 2009
PubMed
Summary
This summary is machine-generated.

The penalized least squares method (SCAD) offers efficient variable selection in regression. However, generalized cross-validation poorly selects tuning parameters, leading to overfitting. A new Bayesian Information Criterion (BIC) selector consistently identifies the true model.

More Related Videos

ARL Spectral Fitting as an Application to Augment Spectral Data via Franck-Condon Lineshape Analysis and Color Analysis
07:11

ARL Spectral Fitting as an Application to Augment Spectral Data via Franck-Condon Lineshape Analysis and Color Analysis

Published on: August 19, 2021

Design and Characterization Methodology for Efficient Wide Range Tunable MEMS Filters
15:25

Design and Characterization Methodology for Efficient Wide Range Tunable MEMS Filters

Published on: February 4, 2018

Related Experiment Videos

Last Updated: Jun 24, 2026

Experimental and Data Analysis Workflow for Soft Matter Nanoindentation
13:04

Experimental and Data Analysis Workflow for Soft Matter Nanoindentation

Published on: January 18, 2022

ARL Spectral Fitting as an Application to Augment Spectral Data via Franck-Condon Lineshape Analysis and Color Analysis
07:11

ARL Spectral Fitting as an Application to Augment Spectral Data via Franck-Condon Lineshape Analysis and Color Analysis

Published on: August 19, 2021

Design and Characterization Methodology for Efficient Wide Range Tunable MEMS Filters
15:25

Design and Characterization Methodology for Efficient Wide Range Tunable MEMS Filters

Published on: February 4, 2018

Area of Science:

  • Statistics
  • Econometrics

Background:

  • Penalized least squares with smoothly clipped absolute deviation (SCAD) penalty is a robust regression shrinkage and selection method.
  • SCAD efficiently selects important variables and yields oracle estimators, but relies on appropriate tuning parameter selection.

Purpose of the Study:

  • To evaluate the effectiveness of generalized cross-validation (GCV) for SCAD tuning parameter selection.
  • To propose and validate a new tuning parameter selection method for SCAD.

Main Methods:

  • Analysis of SCAD regression with a focus on tuning parameter selection.
  • Comparison of generalized cross-validation (GCV) and a proposed Bayesian Information Criterion (BIC) based selector.
  • Simulation studies to assess model selection performance.
  • Application to the Female Labor Supply dataset.

Main Results:

  • Generalized cross-validation (GCV) demonstrates a non-ignorable overfitting effect, failing to select tuning parameters satisfactorily.
  • The proposed BIC tuning parameter selector consistently identifies the true model.
  • Simulation studies support the theoretical findings regarding the superiority of the BIC selector.

Conclusions:

  • The BIC tuning parameter selector offers a reliable method for SCAD regression, overcoming limitations of GCV.
  • Accurate tuning parameter selection is crucial for the performance of SCAD regression models.
  • The proposed method enhances the practical applicability of SCAD in statistical modeling and empirical analysis.