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

Noncompartmental Analysis: Mean Residence Time01:05

Noncompartmental Analysis: Mean Residence Time

According to statistical moment theory, mean residence time (MRT) is an important measure in pharmacokinetics. MRT can be defined as the expected mean of a probability density function distribution. It provides valuable insights into drug disposition in the body.
After the administration of a drug through intravenous bolus injection, the drug molecules are distributed throughout the body and remain there for varying periods. The MRT represents the average time these drug molecules stay in the...
Regression Toward the Mean01:52

Regression Toward the Mean

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 researchers try to extrapolate results...
Estimating Population Mean with Unknown Standard Deviation01:22

Estimating Population Mean with Unknown Standard Deviation

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 Guinness...
Mechanistic Models: Compartment Models in Individual and Population Analysis01:23

Mechanistic Models: Compartment Models in Individual and Population Analysis

Mechanistic models are utilized in individual analysis using single-source data, but imperfections arise due to data collection errors, preventing perfect prediction of observed data. The mathematical equation involves known values (Xi), observed concentrations (Ci), measurement errors (εi), model parameters (ϕj), and the related function (ƒi) for i number of values. Different least-squares metrics quantify differences between predicted and observed values. The ordinary least squares (OLS)...
Kaplan-Meier Approach01:24

Kaplan-Meier Approach

The Kaplan-Meier estimator is a non-parametric method used to estimate the survival function from time-to-event data. In medical research, it is frequently employed to measure the proportion of patients surviving for a certain period after treatment. This estimator is fundamental in analyzing time-to-event data, making it indispensable in clinical trials, epidemiological studies, and reliability engineering. By estimating survival probabilities, researchers can evaluate treatment effectiveness,...
Parametric Survival Analysis: Weibull and Exponential Methods01:14

Parametric Survival Analysis: Weibull and Exponential Methods

Parametric survival analysis models survival data by assuming a specific probability distribution for the time until an event occurs. The Weibull and exponential distributions are two of the most commonly used methods in this context, due to their versatility and relatively straightforward application.
Weibull Distribution
The Weibull distribution is a flexible model used in parametric survival analysis. It can handle both increasing and decreasing hazard rates, depending on its shape parameter...

You might also read

Related Articles

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

Sort by
Same journal

Causally-interpretable random-effects meta-analysis.

Biometrics·2026
Same journal

Subgroup identification via Interaction Tree and Mixed Model for Repeated Measures with application to Alzheimer's disease.

Biometrics·2026
Same journal

Finite mixtures of linear quantile regressions with concomitant variables: a solution to endogeneity in longitudinal data modeling.

Biometrics·2026
Same journal

Discussion on "INTACT: a method for integration of longitudinal physical activity data from multiple sources" by Jingru Zhang, Erjia Cui, Hongzhe Li, and Haochang Shou.

Biometrics·2026
Same journal

A Bayesian phase I/II platform design with data augmentation accounting for delayed outcomes.

Biometrics·2026
Same journal

Rejoinder to the discussion on "INTACT: A method for integration of longitudinal physical activity data from multiple sources".

Biometrics·2026
See all related articles
  1. Home
  3. Statistical Inference For Mean Function Of Partially Observed Functional Time Series.
  1. Home
  3. Statistical Inference For Mean Function Of Partially Observed Functional Time Series.

Related Experiment Video

A Method of Trigonometric Modelling of Seasonal Variation Demonstrated with Multiple Sclerosis Relapse Data
10:46

A Method of Trigonometric Modelling of Seasonal Variation Demonstrated with Multiple Sclerosis Relapse Data

Published on: December 9, 2015

Statistical inference for mean function of partially observed functional time series.

Shuang Sun1, Leheng Cai2, Qirui Hu3,4

  • 1Department of Biostatistics, Epidemiology and Informatics, University of Pennsylvania, 19104, Philadelphia, USA.

Biometrics
|June 22, 2026

View abstract on PubMed

Summary
This summary is machine-generated.

We present a statistical framework for analyzing partially observed functional time series data. Our methods provide reliable statistical inference, including confidence bands and hypothesis tests, even with noisy measurements.

Keywords:
Skorokhod spacefunctional datamissing datarelevant hypothesis testsimultaneous confidence band

More Related Videos

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

Using Eye Movements Recorded in the Visual World Paradigm to Explore the Online Processing of Spoken Language
09:27

Using Eye Movements Recorded in the Visual World Paradigm to Explore the Online Processing of Spoken Language

Published on: October 13, 2018

Related Experiment Videos

A Method of Trigonometric Modelling of Seasonal Variation Demonstrated with Multiple Sclerosis Relapse Data
10:46

A Method of Trigonometric Modelling of Seasonal Variation Demonstrated with Multiple Sclerosis Relapse Data

Published on: December 9, 2015

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

Using Eye Movements Recorded in the Visual World Paradigm to Explore the Online Processing of Spoken Language
09:27

Using Eye Movements Recorded in the Visual World Paradigm to Explore the Online Processing of Spoken Language

Published on: October 13, 2018

Area of Science:

  • Statistics
  • Time Series Analysis
  • Functional Data Analysis

Background:

  • Functional time series data are increasingly common in various scientific fields.
  • Analyzing partially observed or noisy functional data presents significant statistical challenges.
  • Existing methods often struggle with the complexities of incomplete or error-prone functional time series.

Purpose of the Study:

  • To develop a robust statistical framework for inference on mean functions of partially observed functional time series.
  • To address both ideal (noiseless) and practical (noisy) scenarios of data observation.
  • To enable advanced statistical inference techniques tailored for functional time series.

Main Methods:

  • Establish weak convergence for an ideal estimator in the Skorokhod space for noiseless data.
  • Propose a B-spline estimator for noisy data and derive its asymptotic distribution using Gaussian approximation.
  • Utilize multiplier bootstrap for approximating limiting distributions and ensuring procedure consistency.

    • Main Results:

    • Theoretical results establish the asymptotic behavior of the proposed estimators.
    • Development of simultaneous confidence bands, two-sample tests, and hypothesis testing under the supremum norm.
    • Demonstration of the multiplier bootstrap's consistency for practical implementation.

    Conclusions:

    • The developed statistical framework provides a powerful tool for analyzing partially observed functional time series.
    • The proposed methods are validated through numerical experiments and applied successfully to real-world electroencephalogram data.
    • The study contributes novel statistical inference techniques applicable to complex functional data analysis.