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What does best in best linear unbiased estimator refer to?
The term best linear unbiased estimator (BLUE) comes from application of the general notion of unbiased and efficient estimation in the context of linear estimation. In other words, we require the expected value of estimates produced by an estimator to be equal to the true value of population parameters.
What is a linear estimator?
A linear estimator of is a linear combination. in which the coefficients are not allowed to depend on the underlying coefficients , since those are not observable, but are allowed to depend on the values , since these data are observable. (
Which is the best linear unbiased estimator for T ′ β?
In many problems it is of interest to estimate linear combinations of β0,…, βp-1, say, t′β, where tis any nonzero p× 1 vector of known constants. In the next definition the “best” linear unbiased estimatorof t′β is identified.
How is the linearity constraint used in BLUE estimator?
Linearity constraint was already given above. Just repeated here for convenience. For the estimate to be considered unbiased, the expectation (mean) of the estimate must be equal to the true value of the estimate. Now, the million dollor question is : “When can we meet both the constraints ?
When does an estimate need to be unbiased?
For the estimate to be considered unbiased, the expectation (mean) of the estimate must be equal to the true value of the estimate. Now, the million dollor question is : “When can we meet both the constraints ? “. We can meet both the constraints only when the observation is linear.
How is the BLUE estimator used for gaussianwaves?
As the BLUE restricts the estimator to be linear in data, the estimate of the parameter can be written as linear combination of data samples with some weights Here is a vector of constants whose value we seek to find in order to meet the design specifications. Thus, the entire estimation problem boils down to finding the vector of constants – .