SI&DA - Lecture 4 'Estimation Theory - Part I'

SI&DA - Estimation Problem

Estimation Problem

Where $\theta$ can be defined as: → a parameter → a RV

1. TODO Parametric Estimation
2. TODO Bayesian Estimation

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SI&DA - Parametric Estimation

Parametric Estimation

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SI&DA - Definition of 'Estimator'

Definition of ‘Estimator’

SIandDADefinition

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SI&DA - Definition of 'Unbiased Estimator'

Definition of ‘Unbiased Estimator’

SIandDADefinitionExample

Where: → We want to estimate $X$, based on the observation $y$ of a RV $Y$

Another definition:

So that $E[T(Y)]$ converges to our searched parameter $\theta$, more information on theta can be found in: → SI&DA - Estimation Problem → SI&DA - Parametric Estimation →TODO Bayesian Estimation

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~Ex.: Biased and Unbiased result

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~Ex.: Sample Mean

SIandDAExample

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~Ex.: Another Unbiased Estimator

SIandDAExample

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~Ex.: Sample Variance

SIandDAExample

The “BASED Sample Variance”:

It’s a BASED Estimator of the variance: → Dim.:

The “Sample Variance” Estimator (UNBIASED):

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~Ex.: Homework (3)

SIandDAHomework

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SI&DA - Definition of 'Consistent Estimator'

Definition of ‘Consistent Estimator’

SIandDAExample

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~Ex.:

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SI&DA - Theorem 'Sequence of Unbiased Estimators'

Theorem ‘Sequence of Unbiased Estimators’

SIandDATheorem

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~Ex.: Consistency of the Sample Mean

SIandDAExample →TODO Theorem ‘Sequence of Unbiased Estimators’

→ SI&DA - Theorem ‘Law of Large Numbers’

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SI&DA - Theorem 'Law of Large Numbers'

Theorem ‘Law of Large Numbers’

SIandDATheorem

NOTE:

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