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

Regression Toward the Mean01:52

Regression Toward the Mean

6.3K
Regression toward the mean (“RTM”) is a phenomenon in which extremely high or low values—for example, and individual’s blood pressure at a particular moment—appear closer to a group’s average upon remeasuring. Although this statistical peculiarity is the result of random error and chance, it has been problematic across various medical, scientific, financial and psychological applications. In particular, RTM, if not taken into account, can interfere when...
6.3K
Residuals and Least-Squares Property01:11

Residuals and Least-Squares Property

7.2K
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...
7.2K
One-Compartment Open Model: Wagner-Nelson and Loo Riegelman Method for ka Estimation01:24

One-Compartment Open Model: Wagner-Nelson and Loo Riegelman Method for ka Estimation

324
This lesson introduces two critical methods in pharmacokinetics, the Wagner-Nelson and Loo-Riegelman methods, used for estimating the absorption rate constant (ka) for drugs administered via non-intravenous routes. The Wagner-Nelson method relates ka to the plasma concentration derived from the slope of a semilog percent unabsorbed time plot. However, it is limited to drugs with one-compartment kinetics and can be impacted by factors like gastrointestinal motility or enzymatic degradation.
On...
324
Estimating Population Mean with Unknown Standard Deviation01:22

Estimating Population Mean with Unknown Standard Deviation

7.6K
In practice, we rarely know the population standard deviation. In the past, when the sample size was large, this did not present a problem to statisticians. They used the sample standard deviation s as an estimate for σ and proceeded as before to calculate a confidence interval with close enough results. However, statisticians ran into problems when the sample size was small. A small sample size caused inaccuracies in the confidence interval.
William S. Gosset (1876–1937) of the...
7.6K
Multiple Regression01:25

Multiple Regression

2.9K
Multiple regression assesses a linear relationship between one response or dependent variable and two or more independent variables. It has many practical applications.
Farmers can use multiple regression to determine the crop yield based on more than one factor, such as water availability, fertilizer, soil properties, etc. Here, the crop yield is the response or dependent variable as it depends on the other independent variables. The analysis requires the construction of a scatter plot...
2.9K
Estimating Population Mean with Known Standard Deviation01:16

Estimating Population Mean with Known Standard Deviation

8.2K
To construct a confidence interval for a single unknown population mean μ, where the population standard deviation is known, we need sample mean as an estimate for μ and we need the margin of error. Here, the margin of error (EBM) is called the error bound for a population mean (abbreviated EBM). The sample mean is the point estimate of the unknown population mean μ.
The confidence interval estimate will have the form as follows:
(point estimate - error bound, point estimate +...
8.2K

You might also read

Related Articles

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

Sort by
Same author

Nonparametric inference for the localization receiver operating characteristic curve and its extension to free-response image localization tasks.

Statistical methods in medical research·2026
Same author

Copas-Heckman-Type Sensitivity Analysis for Publication Bias in Rare-Event Meta-Analysis Under Generalized Linear Mixed Models.

Statistics in medicine·2026
Same author

Clinical Value of Circulating Endometrial Cells in the Diagnosis and Stratified Diagnosis of Endometriosis.

Journal of clinical medicine·2026
Same author

Evaluation of AI-Based Medical Device Concerning Localization Information Using Nonparametric Inference for the Alternative Free-Response ROC Curve.

Statistics in medicine·2026
Same author

Sensitivity Analysis for Publication Bias in Diagnostic Meta-Analysis of Sparsity Using the Copas t-Statistic Selection Function.

Statistics in medicine·2026
Same author

Biomarker Combination Based on the Youden Index With and Without Gold Standard.

Statistics in medicine·2025

Related Experiment Video

Updated: May 23, 2025

Identification of Disease-related Spatial Covariance Patterns using Neuroimaging Data
14:27

Identification of Disease-related Spatial Covariance Patterns using Neuroimaging Data

Published on: June 26, 2013

15.6K

Positive-definite regularized estimation for high-dimensional covariance on scalar regression.

Jie He1, Yumou Qiu2,3, Xiao-Hua Zhou4,5

  • 1School of Mathematics, Nanjing University of Aeronautics and Astronautics, Nanjing 211106, China.

Biometrics
|March 8, 2025
PubMed
Summary

This study introduces a novel regularized method to model complex, high-dimensional covariance matrices, addressing heterogeneity in subject covariances. The approach ensures sparsity and positive definiteness, crucial for robust statistical analysis.

Keywords:
ADMM algorithmconditional average covariance matrixfMRI datahigh dimensionalitypositive-definiteness constraintregularization

More Related Videos

A Psychophysics Paradigm for the Collection and Analysis of Similarity Judgments
08:12

A Psychophysics Paradigm for the Collection and Analysis of Similarity Judgments

Published on: March 1, 2022

2.4K
O-cresol Concentration Online Measurement Based On Near Infrared Spectroscopy Via Partial Least Square Regression
06:50

O-cresol Concentration Online Measurement Based On Near Infrared Spectroscopy Via Partial Least Square Regression

Published on: November 8, 2019

6.5K

Related Experiment Videos

Last Updated: May 23, 2025

Identification of Disease-related Spatial Covariance Patterns using Neuroimaging Data
14:27

Identification of Disease-related Spatial Covariance Patterns using Neuroimaging Data

Published on: June 26, 2013

15.6K
A Psychophysics Paradigm for the Collection and Analysis of Similarity Judgments
08:12

A Psychophysics Paradigm for the Collection and Analysis of Similarity Judgments

Published on: March 1, 2022

2.4K
O-cresol Concentration Online Measurement Based On Near Infrared Spectroscopy Via Partial Least Square Regression
06:50

O-cresol Concentration Online Measurement Based On Near Infrared Spectroscopy Via Partial Least Square Regression

Published on: November 8, 2019

6.5K

Area of Science:

  • Statistics
  • Machine Learning
  • Neuroscience

Background:

  • Covariance measures marginal dependence but modeling high-dimensional, heterogeneous covariances is challenging.
  • Existing methods struggle with the large parameter space and positive-definiteness constraints of covariance matrices.

Purpose of the Study:

  • To propose a regularized estimation method for regression coefficients of covariances.
  • To address constraints for positive definiteness in conditional average covariance matrices.
  • To develop an estimator that simultaneously achieves sparsity and positive definiteness.

Main Methods:

  • A regularized estimation method for regression coefficients of covariances.
  • Incorporation of sufficient and necessary constraints for positive definiteness.
  • An alternating direction method of multipliers (ADMM) algorithm to solve the optimization problem.

Main Results:

  • The proposed estimator satisfies both sparsity and positive-definite properties.
  • Convergence of the ADMM algorithm is demonstrated.
  • Convergence rates for regression coefficients and heterogeneous covariances are derived.

Conclusions:

  • The novel method effectively models high-dimensional, heterogeneous covariances.
  • The ADMM algorithm provides a robust solution for the constrained optimization problem.
  • The approach is validated through simulations and a brain connectivity case study.