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

Decomposing the Variance in Reading Comprehension to Reveal the Unique and Common Effects of Language and Decoding06:33

Decomposing the Variance in Reading Comprehension to Reveal the Unique and Common Effects of Language and Decoding

7.2K
Here we present a protocol for decomposing the variance in reading comprehension into the unique and common effects of language and...
7.2K
Basic Three-Dimensional (3D) Intestinal Model System with an Immune Component07:39

Basic Three-Dimensional (3D) Intestinal Model System with an Immune Component

1.9K
Here we describe constructing a basic three-dimensional (3D) intestinal cell line model system and a paraffin embedding protocol for light microscopic evaluation of fixed intestinal equivalents. Staining of selected proteins permits the analysis of multiple visual parameters from a single experiment for potential use in preclinical drug screening...
1.9K
Distributions to Estimate Population Parameter01:26

Distributions to Estimate Population Parameter

5.0K
The accurate values of population parameters such as population proportion, population mean, and population standard deviation (or variance) are usually unknown. These are fixed values that can only be estimated from the data collected from the samples. The estimates of each of these parameters are sample proportion, the sample mean, and sample standard deviation (or variance). To obtain the values of these sample statistics, data are required that have particular distribution and central...
5.0K
Development of an Individual-Tree Basal Area Increment Model using a Linear Mixed-Effects Approach04:35

Development of an Individual-Tree Basal Area Increment Model using a Linear Mixed-Effects Approach

3.7K
Mixed-effects models are flexible and useful tools for analyzing data with a hierarchical stochastic structure in forestry and could also be used to significantly improve the performance of forest growth models. Here, a protocol is presented that synthesizes information relating to linear mixed-effects...
3.7K
Variance01:15

Variance

12.0K
The deviations show how spread out the data are about the mean. A positive deviation occurs when the data value exceeds the mean, whereas a negative deviation occurs when the data value is less than the mean. If the deviations are added, the sum is always zero. So one cannot simply add the deviations to get the data spread. By squaring the deviations, the numbers are made positive; thus, their sum will also be positive.
The standard deviation measures the spread in the same units as the data....
12.0K
Use of Principal Components for Scaling Up Topographic Models to Map Soil Redistribution and Soil Organic Carbon09:44

Use of Principal Components for Scaling Up Topographic Models to Map Soil Redistribution and Soil Organic Carbon

10.7K
Landscape processes are critical components of soil formation and play important roles in determining soil properties and spatial structure in landscapes. We propose a new approach using stepwise principal component regression to predict soil redistribution and soil organic carbon across various spatial...
10.7K

You might also read

Related Articles

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

Sort by
Same author

LncRNA SNHG20 silencing inhibits hepatocellular carcinoma progression by sponging miR-5095 from MBD1.

American journal of translational research·2023
Same author

Prolonged 3D culture unlocks black box of primate embryogenesis.

Cell stem cell·2023
Same author

RETN gene polymorphisms interact with alcohol dependence in association with depression.

Journal of clinical laboratory analysis·2023
Same author

Vaccination prevents severe COVID-19 outcome in patients with neutralizing type 1 interferon autoantibodies.

iScience·2023
Same author

Visualization of a gallbladder neuroendocrine carcinoma using a novel peroral cholangioscope.

Endoscopy·2023
Same author

Comparative efficacy of novel-drugs combined therapeutic regimens on relapsed/refractory multiple myeloma: a network meta-analysis.

Hematology (Amsterdam, Netherlands)·2023

Related Experiment Video

Updated: Jan 20, 2026

Decomposing the Variance in Reading Comprehension to Reveal the Unique and Common Effects of Language and Decoding
06:33

Decomposing the Variance in Reading Comprehension to Reveal the Unique and Common Effects of Language and Decoding

Published on: October 11, 2018

7.2K

EIGENVALUE DISTRIBUTIONS OF VARIANCE COMPONENTS ESTIMATORS IN HIGH-DIMENSIONAL RANDOM EFFECTS MODELS.

Fan Zhou1, Iain M Johnstone2

  • 1Department of Statistics and Data Science, Yale University, 24 Hillhouse Avenue, New Haven, CT 06511, zhou.fan@yale.edu.

Annals of Statistics
|August 30, 2019
PubMed
Summary

We developed a new method to approximate the spectra of MANOVA estimators in complex models. This technique, using free probability theory, aids in understanding covariance components in quantitative genetics.

Keywords:
covariance estimationdeterministic equivalentsfree probabilityrandom matrix theory

More Related Videos

Author Spotlight: Investigating the Effects of Compounds on Intestinal Tissue Using 3D Human Cell Line Models
07:39

Author Spotlight: Investigating the Effects of Compounds on Intestinal Tissue Using 3D Human Cell Line Models

Published on: September 1, 2023

1.9K
Development of an Individual-Tree Basal Area Increment Model using a Linear Mixed-Effects Approach
04:35

Development of an Individual-Tree Basal Area Increment Model using a Linear Mixed-Effects Approach

Published on: July 3, 2020

3.7K

Related Experiment Videos

Last Updated: Jan 20, 2026

Decomposing the Variance in Reading Comprehension to Reveal the Unique and Common Effects of Language and Decoding
06:33

Decomposing the Variance in Reading Comprehension to Reveal the Unique and Common Effects of Language and Decoding

Published on: October 11, 2018

7.2K
Author Spotlight: Investigating the Effects of Compounds on Intestinal Tissue Using 3D Human Cell Line Models
07:39

Author Spotlight: Investigating the Effects of Compounds on Intestinal Tissue Using 3D Human Cell Line Models

Published on: September 1, 2023

1.9K
Development of an Individual-Tree Basal Area Increment Model using a Linear Mixed-Effects Approach
04:35

Development of an Individual-Tree Basal Area Increment Model using a Linear Mixed-Effects Approach

Published on: July 3, 2020

3.7K

Area of Science:

  • Statistics
  • Quantitative Genetics
  • Multivariate Analysis

Background:

  • Multivariate random effects models are crucial for analyzing complex data.
  • Estimating variance components and covariance matrices is challenging, especially with high-dimensional data.
  • Current methods struggle when observation dimensionality approaches the number of random effect realizations.

Purpose of the Study:

  • To analyze the spectral distribution of MANOVA estimators for variance component covariance matrices.
  • To develop a theoretical framework for understanding estimator spectra in high-dimensional settings.
  • To provide practical tools for covariance estimation in quantitative genetics.

Main Methods:

  • Operator-valued free probability theory.
  • Asymptotic freeness of rectangular orthogonally-invariant random matrices.
  • Characterization of empirical spectra via deterministic laws and Stieltjes transforms.
  • Numerical solution of fixed-point equations using iterative procedures.

Main Results:

  • Empirical spectra of MANOVA estimators are well-approximated by deterministic laws under specific conditions.
  • Stieltjes transforms of these laws are determined by solvable fixed-point equations.
  • A general asymptotic freeness result for random matrices is established.

Conclusions:

  • The study provides a robust theoretical and numerical framework for analyzing MANOVA estimator spectra.
  • The findings are directly applicable to estimating covariance components in quantitative genetics.
  • The developed methods offer improved understanding and estimation in high-dimensional multivariate models.