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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.
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While taking the arithmetic, geometric, or harmonic mean of a sample data set, equal importance is assigned to all the data points. However, all the values may not always be equally important in some data sets. An intrinsic bias might make it more important to give more weightage to specific values over others.
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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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The range rule of thumb in statistics helps us calculate a dataset's minimum and maximum values with known standard deviation. This rule is based on the concept that 95% of all values in a dataset lie within two standard deviations from the mean.
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Wald-Wolfowitz Runs Test I01:17

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The Wald-Wolfowitz test, also known as the runs test, is a nonparametric statistical test used to assess the randomness of a sequence of two different types of elements (e.g., positive/negative values, successes/failures). It examines whether the order of the elements in a sequence is random or if there is a pattern or trend present. This nonparametric test applies to any ordered data despite the population and sample data distribution, even if a higher sample size is available.
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Updated: Sep 22, 2025

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Distributionally robust mean-absolute deviation portfolio optimization using wasserstein metric.

Dali Chen1, Yuwei Wu2, Jingquan Li1

  • 1School of Management and Engineering, Nanjing University, Nanjing, 210093 China.

Journal of Global Optimization : an International Journal Dealing with Theoretical and Computational Aspects of Seeking Global Optima and Their Applications in Science, Management and Engineering
|May 23, 2022
PubMed
Summary
This summary is machine-generated.

This study introduces a Wasserstein metric-based approach for robust portfolio selection, enhancing decision-making under data uncertainty. The new model, distributionally robust mean-absolute deviation (DR-MAD), offers superior profitability and stability compared to traditional methods.

Keywords:
MAD portfolio modelNonconvex optimizationUncertainty modellingWasserstein distributionally robust optimization

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Area of Science:

  • Quantitative Finance
  • Optimization Theory
  • Financial Modeling

Background:

  • Data uncertainty significantly impacts portfolio selection accuracy.
  • The classic mean-absolute deviation (MAD) model is widely used but sensitive to data variations.
  • Robust decision-making is crucial for reliable investment strategies.

Purpose of the Study:

  • To propose a novel distributionally robust mean-absolute deviation (DR-MAD) model using Wasserstein metrics.
  • To address the non-convexity and infinite-dimensional challenges of robust optimization.
  • To enhance portfolio selection under data uncertainty.

Main Methods:

  • Developed a Wasserstein metric-based data-driven DR-MAD model.
  • Transformed the non-convex problem into two finite-dimensional linear programs.
  • Compared DR-MAD with 1/N, classic MAD, and mean-variance models using S&P 500 stocks.

Main Results:

  • The DR-MAD model was successfully transformed into solvable linear programs.
  • Portfolios from DR-MAD demonstrated superior profitability and stability versus benchmarks.
  • Performance was evaluated across six different market settings.

Conclusions:

  • The Wasserstein distributionally robust optimization framework effectively tackles data uncertainty in portfolio optimization.
  • DR-MAD offers a computationally efficient and robust alternative to existing models.
  • This approach provides enhanced performance in fluctuating market conditions.