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Related Concept Videos

Variance01:15

Variance

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.
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...
Estimating Population Standard Deviation01:26

Estimating Population Standard Deviation

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...
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

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...
Estimating Population Mean with Known Standard Deviation01:16

Estimating Population Mean with Known Standard Deviation

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 + error bound)
The...
Distributions to Estimate Population Parameter01:26

Distributions to Estimate Population Parameter

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...

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

Published on: July 3, 2020

Variance Estimation in a Model with Gaussian Sub-Models.

Vanja M Dukić, Edsel A Peña

    Journal of the American Statistical Association
    |March 4, 2010
    PubMed
    Summary
    This summary is machine-generated.

    Estimating dispersion in Gaussian models is improved by using two-step or weighted estimators that leverage sub-model structures. These methods offer efficiency gains, especially with fewer sub-models, but performance varies with model complexity and distinctiveness.

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    Area of Science:

    • Statistics
    • Statistical Modeling

    Background:

    • Gaussian models are widely used in statistical analysis.
    • Estimating the dispersion parameter is crucial for model inference.
    • The choice between fixed and unknown mean parameters impacts estimation.

    Purpose of the Study:

    • To investigate dispersion parameter estimation in Gaussian models.
    • To analyze the impact of model selection on parameter estimation.
    • To compare the performance of different estimator types.

    Main Methods:

    • Classified estimators into global, two-step, and weighted types.
    • Employed theoretical analysis and simulations.
    • Utilized risk functions based on a scale-invariant quadratic loss function.

    Main Results:

    • Two-step and weighted estimators exploit sub-model structure for efficiency gains, particularly with few sub-models.
    • Efficiency gains may decrease with more sub-models or smaller distances between them.
    • Weighted estimators outperform two-step estimators when sub-models are numerous or close; two-step estimators are better for distinguishable sub-models.

    Conclusions:

    • Exploiting sub-model structure offers advantages in dispersion estimation.
    • The choice of estimator depends on the number and distinctiveness of sub-models.
    • Findings have implications for model averaging and selection strategies.