Summary of Lecture 06 : Basic Concepts of Point Estimations-IV
The video introduces efficiency in estimators, discussing biases, mean absolute error, and mean squared error as measures of goodness. It explains uniformly minimum variance unbiased estimators (UMVUE) and their necessary conditions, uniqueness, and linearity properties. An example in a linear model setting is provided.
### Methodology:
- Introduction of efficiency in estimators
- Consideration of bias, mean absolute error, and mean squared error as measures of goodness in estimators
- Discussion on uniformly minimum variance unbiased estimators (UMVUE)
- Presentation of necessary and sufficient conditions for an estimator to be UMVUE
- Exploration of uniqueness and linearity properties of UMVUE
- Application of concepts in a linear model setting
### Speakers:
- Not provided.
Notable Quotes
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23:23
— « Another interesting property about the UMVU is that if t1 and t2 are UMVUs of g1 theta and g2 theta respectively, then a1 t1 plus a2 t2 is UMVU for a1 g1 theta plus a2 g2 theta.
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25:46
— « Expectation of hy is 0 for all beta.
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27:59
— « Lambda prime X prime Y is UMVU of expectation of lambda prime X prime Y. »