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  • STA260 Lecture 08

Method of Moments Estimation Procedure

• Goal:

  • Estimate $k$ unknown parameters ${\theta }_1,\dots ,{\theta }_k$.

• Process:

  • Identify the $1,\dots ,k$ theoretical moments (${\mu }_j^{\prime }$).
  • Identify the sample moments ($m_j^{\prime }$).

• Algorithm:

  • Equate theoretical moments to sample moments for $j=1\dots k$:
    • ${\mu }_j^{\prime }=m_j^{\prime }$.
  • Solve the resulting System of Linear Equations for the parameters.
  • Note: The system may be quadratic or cubic depending on the parameters.

• Comparison to MLE:

  • MOM is algebraically simpler and requires fewer assumptions.
  • Maximum Likelihood Estimation (MLE) Principle is preferred in advanced statistics due to properties like lower variance.

• Footnotes