lacunary - Mathnotes

Statistics

Definition: Statistical Model \@{statistical-model}

TODO: define this.

Definition: Population Parameter \@{population-parameter}

TODO: define this.

Definition: Statistic \@{statistic}

TODO: define this.

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Definition: Estimator \@{estimator}

TODO: define this.

Referenced by (1 direct)

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Definition: Estimate \@{estimate}

TODO: define this.

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Definition: Bias \@{bias}

TODO: define this.

Definition: Unbiased Estimator \@{unbiased-estimator}

TODO: define this.

Sufficient Statistics

Definition: Sufficient Statistic \@{sufficient-statistic}

A function T(X) is said to be a sufficient statistic relative to the family {fθ(x)} if X is conditionally independent of θ given T(X) for any probability distribution on θ, that is, θ→T(X)→X forms a Markov chain.

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Definition: Minimal Sufficient Statistic \@{minimal-sufficient-statistic}

A statistic T(X) is a minimal sufficient statistic relative to {fθ(x)} if it is a function of every other sufficient statistic U.

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Note \@{note-10}

In terms of the Data-Processing Inequality, this implies that

θ→T(X)→U(X)→X.