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

Expected Frequencies in Goodness-of-Fit Tests01:19

Expected Frequencies in Goodness-of-Fit Tests

7.2K
A goodness-of-fit test is conducted to determine whether the observed frequency values are statistically similar to the frequencies expected for the dataset. Suppose the expected frequencies for a dataset are equal such as when predicting the frequency of any number appearing when casting a die. In that case, the expected frequency is the ratio of the total number of observations (n)  to the number of categories (k).
7.2K
Statistical Methods to Analyze Parametric Data: Student t-Test and Goodness-of-Fit Test01:09

Statistical Methods to Analyze Parametric Data: Student t-Test and Goodness-of-Fit Test

5.5K
In parametric statistics, two fundamental tests stand out for their utility and wide application: the Student's t-test and goodness-of-fit tests. These tests provide researchers with a robust method for drawing insights from data, testing hypotheses, and making informed decisions based on their findings.
The Student's t-test is a statistical test that examines if there is a statistically significant difference between the means of two groups. This test is instrumental when dealing with...
5.5K
Friedman Two-way Analysis of Variance by Ranks01:21

Friedman Two-way Analysis of Variance by Ranks

480
Friedman's Two-Way Analysis of Variance by Ranks is a nonparametric test designed to identify differences across multiple test attempts when traditional assumptions of normality and equal variances do not apply. Unlike conventional ANOVA, which requires normally distributed data with equal variances, Friedman's test is ideal for ordinal or non-normally distributed data, making it particularly useful for analyzing dependent samples, such as matched subjects over time or repeated measures...
480
Test for Homogeneity01:23

Test for Homogeneity

2.4K
The goodness–of–fit test can be used to decide whether a population fits a given distribution, but it will not suffice to decide whether two populations follow the same unknown distribution. A different test, called the test for homogeneity, can be used to conclude whether two populations have the same distribution. To calculate the test statistic for a test for homogeneity, follow the same procedure as with the test of independence. The hypotheses for the test for homogeneity can...
2.4K
Correlation of Experimental Data01:23

Correlation of Experimental Data

479
Dimensional analysis simplifies complex physical problems and guides experimental investigations, but it does not provide complete solutions. It identifies the dimensionless groups that influence a phenomenon, but experimental data is needed to establish the specific relationships and validate theoretical predictions.
For example, a spherical particle moving through a viscous fluid experiences drag. Dimensional analysis shows that the drag force depends on the particle's diameter, velocity,...
479
Statistical Inference Techniques in Hypothesis Testing: Parametric Versus Nonparametric Data01:16

Statistical Inference Techniques in Hypothesis Testing: Parametric Versus Nonparametric Data

456
Statistical inference techniques, paramount in hypothesis testing, differentiate into two broad categories: parametric and nonparametric statistics.
Parametric statistics, as the name suggests, assumes that data follow a specific distribution, often a normal distribution. This assumption enables robust hypothesis testing and estimation. Parametric methods, like the Student's t-test or Goodness-of-fit test, are frequently employed in biostatistics due to their robustness. For instance,...
456

You might also read

Related Articles

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

Sort by
Same author

Single-cell transcriptomics uncovers endothelial progenitor-like remodelling driving human coronary atherosclerosis progression.

Nature cell biology·2026
Same author

Identification of diagnostic blood indicators associated with adenomyosis: a retrospective cohort study.

Frontiers in endocrinology·2026
Same author

Pharmacokinetic and bioequivalence study of apremilast tablets in healthy Chinese subjects under fasting and fed conditions.

International journal of clinical pharmacology and therapeutics·2026
Same author

Interference Crystallization Rebalances Facet Competition for Efficient and Stable Perovskite Solar Cells.

Advanced materials (Deerfield Beach, Fla.)·2026
Same author

Bilayer Hole-Selective Contact Enhancing Hole Extraction for Efficient Inverted Wide-Bandgap Perovskite Solar Cells.

ACS applied materials & interfaces·2026
Same author

Localized Micro-Solvent Field Engineering for Efficient and Reproducible Quasi-Quantum-Dot Perovskite Light-Emitting Diodes.

Advanced materials (Deerfield Beach, Fla.)·2026

Related Experiment Video

Updated: Jan 17, 2026

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

Covariance test for discretely observed functional data: when and how it works?

Yang Zhou1, Jin Yang2, Fang Yao3

  • 1School of Statistics, Beijing Normal University, Beijing, China.

Arxiv
|September 19, 2025
PubMed
Summary

This study introduces a new covariance test for functional data analysis, addressing noisy, discrete observations. The proposed method offers a robust, nonparametric approach that performs well even with limited data points.

Keywords:
Diverging truncationFunctional principal componentsPerturbation boundsPhase transition

More Related Videos

Basics of Multivariate Analysis in Neuroimaging Data
06:35

Basics of Multivariate Analysis in Neuroimaging Data

Published on: July 24, 2010

17.3K
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

16.1K

Related Experiment Videos

Last Updated: Jan 17, 2026

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
Basics of Multivariate Analysis in Neuroimaging Data
06:35

Basics of Multivariate Analysis in Neuroimaging Data

Published on: July 24, 2010

17.3K
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

16.1K

Area of Science:

  • Statistics
  • Functional Data Analysis
  • Nonparametric Statistics

Background:

  • Existing covariance tests in functional data analysis are limited to fully observed data.
  • Real-world functional data often consists of discrete, noisy trajectories.
  • A gap exists in statistical methods for covariance testing with practical data limitations.

Purpose of the Study:

  • To develop a robust covariance test for functional data with discrete and noisy observations.
  • To extend functional principal component (FPC)-based testing to handle practical data limitations.
  • To establish the theoretical validity and performance of the proposed nonparametric test.

Main Methods:

  • Employing a pool-smoothing strategy to construct an FPC-based test statistic.
  • Allowing the number of estimated eigenfunctions to grow with sample size for a nonparametric approach.
  • Utilizing perturbation bounds of estimated eigenfunctions to validate asymptotic null distribution.

Main Results:

  • The proposed test is consistently nonparametric and asymptotically valid across truncation levels.
  • A phase transition phenomenon is observed where the test performs as if data were fully observed at sufficient sampling frequency.
  • Numerical studies demonstrate favorable performance compared to existing methods for covariance testing.

Conclusions:

  • The developed FPC-based covariance test effectively handles discrete and noisy functional data.
  • The method bridges the gap between theoretical models and practical applications in functional data analysis.
  • The findings offer a valuable tool for researchers working with real-world functional data.