Detection and Estimation Theory Lecture 12 Mojtaba Soltanalian- UIC - - PowerPoint PPT Presentation

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Detection and Estimation Theory Lecture 12 Mojtaba Soltanalian- UIC - - PowerPoint PPT Presentation

Jan 31, 2024 234 likes •440 views

Detection and Estimation Theory Lecture 12 Mojtaba Soltanalian- UIC msol@uic.edu http://msol.people.uic.edu Based on ECE 531 Slides- 2011 (Prof. Natasha Devroye) Summary Need (at least some) information about the pdf. Least Square

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Detection and Estimation Theory Lecture 12

Mojtaba Soltanalian- UIC

msol@uic.edu http://msol.people.uic.edu

Based on ECE 531 Slides- 2011 (Prof. Natasha Devroye)

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Summary

 Need (at least some) information about the pdf.

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Least Square Estimation

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Least Square Estimation

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Least Square Estimation

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Least Square Estimation Basic Examples

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Least Square Estimation Basic Examples

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Least Square Estimation Basic Examples (Regression)

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Least Square Estimation The Linear Case (Theory)

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Least Square Estimation Linear Case: LSE vs Other Estimators

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Least Square Estimation Linear Case: LSE vs Other Estimators

A side remark:

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Weighted Linear LSE

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LSE: A Geometric Interpretation

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LSE: A Geometric Interpretation

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Various Versions of the LSE

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Various Versions of the LSE

….

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Various Versions of the LSE

 A typical example in non-negative least squares

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Various Versions of the LSE

 A typical example in non-negative least squares

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Non-Linear LSE

Another important trick: Linearize! (example)