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Propagation of Uncertainty from Systematic Error01:10

Propagation of Uncertainty from Systematic Error

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The atomic mass of an element varies due to the relative ratio of its isotopes. A sample's relative proportion of oxygen isotopes influences its average atomic mass. For instance, if we were to measure the atomic mass of oxygen from a sample, the mass would be a weighted average of the isotopic masses of oxygen in that sample. Since a single sample is not likely to perfectly reflect the true atomic mass of oxygen for all the molecules of oxygen on Earth, the mass we obtain from this...
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Scientists always try their best to record measurements with the utmost accuracy and precision. However, sometimes errors do occur. These errors can be random or systematic. Random errors are observed due to the inconsistency or fluctuation in the measurement process, or variations in the quantity itself that is being measured. Such errors fluctuate from being greater than or less than the true value in repeated measurements. Consider a scientist measuring the length of an earthworm using a...
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Error is the deviation of the obtained result from the true, expected value or the estimated central value. Errors are expressed in absolute or relative terms.
Absolute error in a measurement is the numerical difference from the true or central value. Relative error is the ratio between absolute error and the true or central value, expressed as a percentage.
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The margin of error is also called the maximum error of an estimate. The margin of error is the maximum possible or expected difference between the observed sample parameter value and the actual population parameter value. For proportion, it is the maximum difference between the value of sample proportion obtained from the data and the true value of population proportion. As the true value of the population parameter is not known, the margin of error is calculated using the sample statistic.
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Propagation of Uncertainty from Random Error00:59

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An experiment often consists of more than a single step. In this case, measurements at each step give rise to uncertainty. Because the measurements occur in successive steps, the uncertainty in one step necessarily contributes to that in the subsequent step. As we perform statistical analysis on these types of experiments, we must learn to account for the propagation of uncertainty from one step to the next. The propagation of uncertainty depends on the type of arithmetic operation performed on...
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In the case of systematic errors, the sources can be identified, and the errors can be subsequently minimized by addressing these sources. According to the source, systematic errors can be divided into sampling, instrumental, methodological, and personal errors.
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Robust Relative Error Estimation.

Kei Hirose1,2, Hiroki Masuda3

  • 1Institute of Mathematics for Industry, Kyushu University, 744 Motooka, Nishi-ku, Fukuoka 819-0395, Japan.

Entropy (Basel, Switzerland)
|December 3, 2020
PubMed
Summary

This study introduces a robust relative error estimation method using a novel gamma-likelihood function. The new approach minimizes sensitivity to outliers in regression analysis, enhancing statistical model reliability.

Keywords:
relative error estimationrobust estimationγ-divergence

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Area of Science:

  • Statistics
  • Robust Statistics
  • Regression Analysis

Background:

  • Existing relative error estimation methods in regression are sensitive to outliers.
  • Outliers can significantly impact the accuracy and reliability of statistical models.

Purpose of the Study:

  • To develop a robust relative error estimation procedure resistant to outliers.
  • To introduce a new method based on the gamma-likelihood function and gamma-cross entropy.

Main Methods:

  • Employing the gamma-likelihood function, derived from gamma-cross entropy.
  • Utilizing a majorize-minimize (MM) algorithm to minimize the negative gamma-likelihood function.
  • Deriving asymptotic normality for the estimator and a consistent estimator for the asymptotic covariance matrix.

Main Results:

  • The proposed estimating equation exhibits a redescending property, crucial for robust statistics.
  • The MM algorithm ensures a decrease in the negative gamma-likelihood function per iteration.
  • Monte Carlo simulations and real data analysis demonstrate the procedure's effectiveness and usefulness.

Conclusions:

  • The novel gamma-likelihood approach provides a robust alternative for relative error estimation in regression.
  • The method offers improved reliability by mitigating outlier sensitivity.
  • The derived asymptotic properties facilitate the construction of approximate confidence sets.