Weighted Covariance: Calculating 3x3 Matrix with Point Weights

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SUMMARY

The discussion centers on calculating a weighted covariance matrix for a dataset consisting of (x, y, z) coordinates, specifically focusing on how to incorporate point weights into the covariance formula. Preet successfully computes the standard covariance but seeks guidance on adapting the formula to account for weights. The reference to the Wikipedia page on sample covariance matrices indicates that the community is looking for a deeper understanding of the derivation of the weighted covariance equation.

PREREQUISITES
  • Understanding of covariance and its mathematical formulation.
  • Familiarity with weighted averages and their application in statistics.
  • Basic knowledge of matrix operations, particularly 3x3 matrices.
  • Experience with statistical software or programming languages capable of matrix calculations, such as Python with NumPy or R.
NEXT STEPS
  • Research the derivation of the weighted covariance formula, focusing on the mathematical principles involved.
  • Explore the implementation of weighted covariance calculations in Python using NumPy or Pandas.
  • Learn about the application of weighted covariance in multivariate statistics and its implications.
  • Investigate alternative methods for handling weighted data in statistical analysis, such as generalized least squares.
USEFUL FOR

Data scientists, statisticians, and researchers working with weighted datasets who need to calculate covariance matrices accurately.

preet
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Hi All,

I have a data set consisting of (x,y,z) coordinates. I can calculate the covariance between them just fine. Calculating all the covariances between the three variables gives me a nice 3x3 matrix. However, the points have a weighting value as well. I don't know how to account for the point weights in the normal covariance formula.

I would appreciate any advice.


Regards,

-Preet
 
Physics news on Phys.org
Thank you. I had seen that link... I don't understand how the equation in the provided link was derived. I we hoping someone could help flesh it out.
 

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