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Related Experiment Videos

Sequentially Estimating the Approximate Conditional Mean Using Extreme Learning Machines.

Lijuan Huo1, Jin Seo Cho1,2

  • 1School of Humanities and Social Sciences, Beijing Institute of Technology, Haidian, Beijing 100081, China.

Entropy (Basel, Switzerland)
|December 8, 2020
PubMed
Summary
This summary is machine-generated.

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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...
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What are Estimates?01:06

What are Estimates?

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It isn't easy to measure a parameter such as the mean height or the mean weight of a population. So, we draw samples from the population and calculate the mean height or mean weight of the individuals in the sample. This sample data acts as a representative measure of the population parameter. These sample statistics are known as estimates. 
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Mechanistic Models: Compartment Models in Algorithms for Numerical Problem Solving01:29

Mechanistic Models: Compartment Models in Algorithms for Numerical Problem Solving

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Mechanistic models play a crucial role in algorithms for numerical problem-solving, particularly in nonlinear mixed effects modeling (NMEM). These models aim to minimize specific objective functions by evaluating various parameter estimates, leading to the development of systematic algorithms. In some cases, linearization techniques approximate the model using linear equations.
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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.
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Expected Value01:15

Expected Value

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The WELM testing procedure, using extreme learning machines, offers a straightforward method for detecting model misspecification in conditional mean models. It accurately identifies the most parsimonious model or rejects all models when none are correct.

Area of Science:

  • Statistics
  • Machine Learning
  • Econometrics

Background:

  • Existing omnibus test statistics for model specification often exhibit inconvenient convergence properties.
  • Detecting model misspecification in conditional mean models is crucial for reliable statistical inference.

Purpose of the Study:

  • To introduce and evaluate the WELM (Wald test with Extreme Learning Machine) testing procedure for model specification.
  • To assess the performance of a sequential WELM testing procedure in selecting parsimonious conditional mean models.

Main Methods:

  • Applied the extreme learning machine (ELM) to construct the Wald test statistic for model specification.
  • Developed a sequential testing procedure using a set of polynomial models and WELM.
  • Conducted extensive Monte Carlo simulations to evaluate the WELM procedure's performance.
Keywords:
conditional mean specification testingconsistent correct model estimationextreme learning machinefunctional regressiongaussian processomnibus testsequential testing procedurewald test statistic

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Main Results:

  • The WELM testing procedure is straightforwardly applicable for detecting model misspecification.
  • The sequential WELM procedure consistently estimates the most parsimonious conditional mean when a correct model exists within the set.
  • The procedure reliably rejects all models if none are correctly specified.

Conclusions:

  • The WELM testing procedure provides a practical and effective tool for model specification testing.
  • The sequential application of WELM enhances the ability to identify the most appropriate conditional mean model in a series.