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

Estimating Population Mean with Known Standard Deviation01:16

Estimating Population Mean with Known Standard Deviation

7.4K
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 +...
7.4K
Estimating Population Mean with Unknown Standard Deviation01:22

Estimating Population Mean with Unknown Standard Deviation

6.4K
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...
6.4K
Estimating Population Standard Deviation01:26

Estimating Population Standard Deviation

2.5K
When the population standard deviation is unknown and the sample size is large, the sample standard deviation s is commonly used as a point estimate of σ. However, it can sometimes under or overestimate the population standard deviation. To overcome this drawback, confidence intervals are determined to estimate population parameters and eliminate any calculation bias accurately. However, this only applies to random samples from normally distributed populations. Knowing the sample mean and...
2.5K
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

1.5K
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...
1.5K
Empirical Method to Interpret Standard Deviation01:09

Empirical Method to Interpret Standard Deviation

8.0K
The empirical rule, also known as the three-sigma rule, allows a statistician to interpret the standard deviation in a normally distributed dataset. The rule states that 68% of the data lies within one standard deviation from the mean, 95% lies within two standard deviations from the mean, and 99.7% lies within three standard deviations from the mean. Additionally, this rule is also called the 68-95-99.7 rule.
This rule is used widely in statistics to calculate the proportion of data values...
8.0K
Distributions to Estimate Population Parameter01:26

Distributions to Estimate Population Parameter

4.5K
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...
4.5K

You might also read

Related Articles

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

Sort by
Same author

Molecular Basis of Synergistic Causal Effect of Dual GLP-1R and GIPR Agonists for Risk Reduction in Diabetic Retinopathy, Alzheimer Disease, and Coronary Artery Disease in Diabetic Patients.

Genes·2026
Same author

A Repeated Block Perturbation Subsampling for Large-Scale Longitudinal Data.

Journal of statistical theory and practice·2026
Same author

Evolving Cancer Characteristics Among World Trade Center Survivors: An Updated Analysis from the WTC Environmental Health Center.

International journal of environmental research and public health·2026
Same author

Association of plasma biomarkers with amyloid and tau PET in pre-dementia stages.

Alzheimer's & dementia : the journal of the Alzheimer's Association·2026
Same author

Sleep duration, blood pressure and cardiovascular outcomes in the middle-aged and the elderly.

International journal of cardiology. Cardiovascular risk and prevention·2026
Same author

Test-retest reliability of FreeSurfer measures of neurodegeneration.

NeuroImage·2026

Related Experiment Video

Updated: Apr 30, 2026

Analyzing Melts and Fluids from Ab Initio Molecular Dynamics Simulations with the UMD Package
06:37

Analyzing Melts and Fluids from Ab Initio Molecular Dynamics Simulations with the UMD Package

Published on: September 17, 2021

5.9K

A Monte Carlo method for variance estimation for estimators based on induced smoothing.

Zhezhen Jin1, Yongzhao Shao2, Zhiliang Ying3

  • 1Department of Biostatistics, Columbia University, New York, NY 10032, USA zj7@columbia.edu.

Biostatistics (Oxford, England)
|May 10, 2014
PubMed
Summary

This study introduces a Monte Carlo method for reliable variance estimation in semiparametric models. The approach ensures consistent variance estimates for complex statistical inference problems.

Keywords:
Accelerated failure time modelAsymptotic fiducialdistributionBuckley–James estimatorCensored dataContraction mappingEstimating functionKaplan–Meier estimatorMonte CarlointegrationRank estimator

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

2.9K
Basics of Multivariate Analysis in Neuroimaging Data
06:35

Basics of Multivariate Analysis in Neuroimaging Data

Published on: July 24, 2010

17.6K

Related Experiment Videos

Last Updated: Apr 30, 2026

Analyzing Melts and Fluids from Ab Initio Molecular Dynamics Simulations with the UMD Package
06:37

Analyzing Melts and Fluids from Ab Initio Molecular Dynamics Simulations with the UMD Package

Published on: September 17, 2021

5.9K
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

2.9K
Basics of Multivariate Analysis in Neuroimaging Data
06:35

Basics of Multivariate Analysis in Neuroimaging Data

Published on: July 24, 2010

17.6K

Area of Science:

  • Statistics
  • Statistical Inference
  • Computational Statistics

Background:

  • Reliable variance estimation is crucial for semiparametric models.
  • Existing methods based on induced smoothing may require explicit forms of estimating functions.
  • Developing robust variance estimators is essential for accurate statistical inference.

Purpose of the Study:

  • To develop a Monte Carlo version of variance estimation for semiparametric models.
  • To provide a method that does not require the explicit form of the estimating function.
  • To establish a general convergence theory for the proposed variance estimation procedure.

Main Methods:

  • A Monte Carlo approach is developed for variance estimation.
  • The method relies on numerical evaluation of the estimating function.
  • A general convergence theory is established to prove consistency and convergence rate.

Main Results:

  • The Monte Carlo method provides consistent variance estimators.
  • One-step iteration guarantees a consistent variance estimator.
  • Continued iterations exhibit exponential convergence rates.
  • The method is successfully applied to Buckley-James and weighted log-rank estimators.

Conclusions:

  • The proposed Monte Carlo method offers a flexible and reliable approach to variance estimation in semiparametric models.
  • This technique enhances statistical inference for censored data and multiple event times.
  • The method's convergence properties ensure accurate and efficient estimation.