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Related Concept Videos

Deconvolution01:20

Deconvolution

Deconvolution, also known as inverse filtering, is the process of extracting the impulse response from known input and output signals. This technique is vital in scenarios where the system's characteristics are unknown, and they must be inferred from the observable signals.
Deconvolution involves several mathematical techniques to derive the impulse response. One common approach is polynomial division. In this method, the input and output sequences are treated as coefficients of...
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 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...
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...
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...
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...

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Development of an Individual-Tree Basal Area Increment Model using a Linear Mixed-Effects Approach
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Deconvolution Estimation in Measurement Error Models: The R Package decon.

Xiao-Feng Wang1, Bin Wang

  • 1Department of Quantitative Health Science/Biostatistics Section, Cleveland Clinic Foundation, 9500 Euclid Ave, Cleveland OH 44195, United States of America.

Journal of Statistical Software
|May 27, 2011
PubMed
Summary
This summary is machine-generated.

This study introduces decon, an R software package for measurement error models. It uses deconvolution kernel methods and fast Fourier transforms for efficient density estimation and regression with contaminated data.

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Area of Science:

  • Statistics
  • Computational Statistics

Background:

  • Measurement error is prevalent across scientific disciplines.
  • Key challenges include density estimation from contaminated data and nonparametric regression with errors-in-variables.

Purpose of the Study:

  • Introduce the decon R package for addressing measurement error models.
  • Provide efficient computational tools for deconvolution kernel estimation.

Main Methods:

  • Utilize deconvolution kernel methods for handling measurement error.
  • Adapt the fast Fourier transform algorithm for computational efficiency.
  • Incorporate functions for both homoscedastic and heteroscedastic errors.

Main Results:

  • The decon package offers a collection of functions for measurement error problems.
  • The implementation leverages fast Fourier transform for efficient deconvolution kernel estimation.
  • Practical guidance on smoothing parameter selection is provided.

Conclusions:

  • The decon package provides a valuable tool for statistical analysis involving measurement error.
  • The software facilitates efficient and practical application of deconvolution methods.
  • Demonstrates utility through simulated and real-world data examples.