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Related Concept Videos

Mean Absolute Deviation01:13

Mean Absolute Deviation

The mean absolute deviation is also a measure of the variability of data in a sample. It is the absolute value of the average difference between the data values and the mean.
Let us consider a dataset containing the number of unsold cupcakes in five shops: 10, 15, 8, 7, and 10. Initially, calculate the sample mean. Then calculate the deviation, or the difference, between each data value and the mean. Next, the absolute values of these deviations are added and divided by the sample size to...
Types of Errors: Detection and Minimization01:12

Types of Errors: Detection and Minimization

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.
Errors can be classified by source, magnitude, and sign. There are three types of errors: systematic, random, and gross.
Systematic or...
Residuals and Least-Squares Property01:11

Residuals and Least-Squares Property

The vertical distance between the actual value of y and the estimated value of y. In other words, it measures the vertical distance between the actual data point and the predicted point on the line
If the observed data point lies above the line, the residual is positive, and the line underestimates the actual data value for y. If the observed data point lies below the line, the residual is negative, and the line overestimates the actual data value for y.
The process of fitting the best-fit...
Propagation of Uncertainty from Random Error00:59

Propagation of Uncertainty from Random Error

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...
Uncertainty in Measurement: Accuracy and Precision03:37

Uncertainty in Measurement: Accuracy and Precision

Scientists typically make repeated measurements of a quantity to ensure the quality of their findings and to evaluate both the precision and the accuracy of their results. Measurements are said to be precise if they yield very similar results when repeated in the same manner. A measurement is considered accurate if it yields a result that is very close to the true or the accepted value. Precise values agree with each other; accurate values agree with a true value.
Uncertainty: Overview00:59

Uncertainty: Overview

In analytical chemistry, we often perform repetitive measurements to detect and minimize inaccuracies caused by both determinate and indeterminate errors. Despite the cares we take, the presence of random errors means that repeated measurements almost never have exactly the same magnitude. The collective difference between these measurements - observed values - and the estimated or expected value is called uncertainty. Uncertainty is conventionally written after the estimated or expected value.

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Doppler Ultrasound-Based Leg Blood Flow Assessment During Single-Leg Knee-Extensor Exercise in an Uncontrolled Setting
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Least Absolute Relative Error Estimation.

Kani Chen1, Shaojun Guo2, Yuanyuan Lin3

  • 1Department of Mathematics, HKUST, Kowloon, Hong Kong, China (makchen@ust.hk).

Journal of the American Statistical Association
|September 10, 2013
PubMed
Summary
This summary is machine-generated.

This study introduces a new method for analyzing multiplicative regression models by minimizing relative errors, offering a more practical approach for financial and biomedical data. The method proves consistent and asymptotically normal, enhancing statistical estimation for positive response variables.

Keywords:
Logarithm transformationMultiplicative regression modelRandom weightingRelative error

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Area of Science:

  • Econometrics
  • Biostatistics
  • Statistical Modeling

Background:

  • Multiplicative regression and accelerated failure time models are vital for analyzing positive response data common in finance and medicine.
  • Traditional methods like least squares and least absolute deviation focus on absolute errors, which may not be optimal for all applications.
  • Practitioners often prioritize relative error, especially in fields like financial market analysis.

Purpose of the Study:

  • To propose and validate a novel estimation method for multiplicative regression models based on minimizing least absolute relative errors.
  • To provide a statistically rigorous framework for this new estimation technique.
  • To demonstrate the practical utility of the proposed method in analyzing real-world financial data.

Main Methods:

  • Developed a least absolute relative errors (LARE) estimation criterion for multiplicative regression models.
  • Proved the consistency and asymptotic normality of the LARE estimator.
  • Introduced an inference approach using random weighting.
  • Identified the optimal error distribution for efficient LARE estimation.

Main Results:

  • The proposed LARE estimation method is shown to be consistent and asymptotically normal.
  • An efficient estimation is achieved when the error distribution is specified.
  • Simulation studies provide supportive evidence for the method's performance.
  • The method is successfully applied to analyze stock returns from the Hong Kong Stock Exchange.

Conclusions:

  • Minimizing least absolute relative errors offers a valuable alternative to traditional methods for multiplicative regression models.
  • The developed statistical framework supports reliable inference for this new estimation approach.
  • The method demonstrates practical applicability and effectiveness in financial data analysis, particularly for stock returns.