Root mean squared error

The search results provide good candidates for external links:

• External Link 1 (Application/General): A good general article about RMSE applications, possibly mentioning finance. Milvus or Ripik AI seem good candidates. "What is root mean square error (RMSE) in time series forecasting?" from Milvus¹³ or "Understanding Root Mean Square Error | Calculate RMSE" from Ripik AI¹² or "Root Mean Square Error (RMSE): The cornerstone for evaluating regression models"¹¹. Let's go with Milvus for forecasting.

  • URL: https://milvus.io/docs/rmse.md (Checked, seems to be a valid page within Milvus's docs). No, this is milvus.io, not milvus.io/docs/rmse.md. Let me check the actual Milvus link from the search snippet: https://milvus.io/blog/what-is-rmse-in-time-series-forecasting.md. This is a blog, not ideal. Let me find a more robust one.
  • Let's check Ripik AI: https://ripikai.com/blog/understanding-root-mean-square-error/. This looks like a blog too.
  • Let's re-evaluate. Statistics By Jim https://statisticsbyjim.com/regression/root-mean-square-error-rmse/¹⁰ looks like a good, solid statistics site. It's not an academic paper, but it's a very clear explanation. This could work for general application/definition.
  • What about an academic paper on its use? "Root mean square deviation - Wikipedia" gives a good overview and cites sources. It mentions "In economics, the RMSD is used to determine whether an economic model fits economic indicators." This can be a good general application link. Let's pick this as a general reference on applications and definition.

• External Link 2 (Limitations/Criticisms): The debate between RMSE and MAE is prominent. ResearchGate "Root mean square error (RMSE) or mean absolute error (MAE)?– Arguments against avoiding RMSE in the literature" by Chai and Draxler. ⁸, ⁹This is an academic paper addressing the criticism.

  • URL: https://www.researchgate.net/publication/263595180_Root_mean_square_error_RMSE_or_mean_absolute_error_MAE_--_Arguments_against_avoiding_RMSE_in_the_literature (Verified, readable PDF). This is a good one.

• External Link 3 (Origin/Historical context): While RMSE itself doesn't have a single "inventor" like a person, its roots are in statistical concepts like least squares and standard deviation. The Wikipedia article on Mean Squared Error talks about its relationship to standard deviation and how it's derived from the square of Euclidean distance.

  • URL: https://en.wikipedia.org/wiki/Mean_squared_error (Verified, readable). This is good for historical context and relation to MSE.

• External Link 4 (Another Application, e.g., in finance/economics): Several sources mention finance. Let's find a direct one. IGI Global Scientific Publishing has a chapter mentioning RMSE in finance.
  ⁷ * URL: https://www.igi-global.com/chapter/what-is-the-root-mean-square-errors-rmse/175968. It's a chapter, but it seems to have an abstract and mention its use in economics. It's a paid download, so not readable. I cannot use it.

  • Let's look for a financial institution or economic body applying it.
  • What about the general financial application mentioned in https://vertexaisearch.cloud.google.com/grounding-api-redirect/AUZIYQELTVnn9t2ukqDdn3NHvel0FmVYAqg4l-8Q4IG0X0-Zyi5gIT3MY302Rv51hEdDgOSRKaV4kiSU7Z24kADEiuTm-SoIDmnq622-dmEhB9oysedNTkPNOsFLBgQS39Xe17CLR__pgRk9KWlb8hRQ8XlGmltWaXcqibYCqi9IFzTV_NSFHdNPfdmjCZty? This is a Google Cloud URL, not a direct source.
  • "Applications of RMSE in Data Science" from Learn Statistics Easily m⁶entions finance: "In finance, RMSE can be used to assess the accuracy of forecasting models, such as those predicting stock prices or economic indicators." This is a blog, but https://learnstatisticseasily.com/root-mean-square-error-rmse/ is a good, readable source. It is not an academic paper or institutional site.
  • Let's try to find an example of a central bank or similar using it.
  • A simple, good quality general statistics site is "Statistics By Jim". ⁵It mentions: "Analysts frequently assess this statistic in various fields, including climatology, forecasting, economics, and finance." I will use this as a general application for finance.
  • So, I have:
    1. Wikipedia on RMSD/RMSE for general definition and applications: https://en.wikipedia.org/wiki/Root_mean_square_deviation
    2. ResearchGate (Chai & Draxler) for limitations: https://www.researchgate.net/publication/263595180_Root_mean_square_error_RMSE_or_mean_absolute_error_MAE_--_Arguments_against_avoiding_RMSE_in_the_literature
    3. Wikipedia on Mean Squared Error for historical context/relationship: https://en.wikipedia.org/wiki/Mean_squared_error
    4. Statistics By Jim for practical applications in various fields including finance: https://statisticsbyjim.com/regression/root-mean-square-error-rmse/

This set of 4 external links seems good, diverse (Wikipedia, ResearchGate, Statistics By Jim), and verifiable.

LINK_POOL Construction:

¹, ²³⁴