SI&DA - Lecture 5 'Estimation Theory - Part II'

SI&DA - Definition of 'MSE (Mean Square Error)'

Definition of ‘MSE (Mean Square Error)’

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SI&DA - Definition of 'MSE Estimator Comparison'

Definition of ‘MSE Estimator Comparison’

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Definition of ‘Uniformly Minimum Variance Unbiased Estimator (UMVUE)’

NOTE: $v$ is a vector, $v\in {\mathbb{R}}^m$ This theorem just says that the matrix $v{v}^T$ is a diagonal matrix, and if we were to sum all the elements in the diagonal the result will be equal to $v^{T}v$. Nothing too surprising.

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Definition of ‘BLUE (Best Linear Unbiased Estimator)’

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~Ex.:

→ Then utilizing the Lagrangian Function:

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Theorem ‘The Cramer-Rao Bound’

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Definition of ‘Efficient Estimator’

→ Where:

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Property the Fisher Information Matrix for i.i.d. RVs

i.i.d. RVs : Independent Identically Distributed Random Variables

$I_n(\theta )$ : Fisher information matrix

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Properties of the Sample Mean

TheTODO Sample Mean is an:

• TODO Efficient Estimator
• TODO UMVU (Uniformly Minimum Variance Unbiased) Estimator

Because itsTODO Fisher Information Matrix matches theTODO Cramer-Rao Bound.

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~Dim.:

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~Ex.:

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