What do you understand by best linear unbiased estimator?
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 the best unbiased estimator?
Definition 12.3 (Best Unbiased Estimator) An estimator W∗ is a best unbiased estimator of τ(θ) if it satisfies EθW∗=τ(θ) E θ W ∗ = τ ( θ ) for all θ and for any other estimator W satisfies EθW=τ(θ) E θ W = τ ( θ ) , we have Varθ(W∗)≤Varθ(W) V a r θ ( W ∗ ) ≤ V a r θ ( W ) for all θ .
What are the conditions under which OLS is the best linear unbiased estimator?
In short: If the estimator is unbiased but doesn’t have the least variance – it’s not the best! If the estimator has the least variance but is biased – it’s again not the best! If the estimator is both unbiased and has the least variance – it’s the best estimator.
Who invented blup?
BLUP was derived by Charles Roy Henderson in 1950 but the term “best linear unbiased predictor” (or “prediction”) seems not to have been used until 1962. “Best linear unbiased predictions” (BLUPs) of random effects are similar to best linear unbiased estimates (BLUEs) (see Gauss–Markov theorem) of fixed effects.
What is meant by the best unbiased?
1 : free from bias especially : free from all prejudice and favoritism : eminently fair an unbiased opinion. 2 : having an expected value equal to a population parameter being estimated an unbiased estimate of the population mean.
What is 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. (
What is blue econometric?
BLUE is an acronym for the following: Best Linear Unbiased Estimator. In this context, the definition of “best” refers to the minimum variance or the narrowest sampling distribution.
Why is OLS the best estimator?
The OLS estimator is one that has a minimum variance. This property is simply a way to determine which estimator to use. An estimator that is unbiased but does not have the minimum variance is not good. An estimator that is unbiased and has the minimum variance of all other estimators is the best (efficient).
What is the difference between blue and BLUP?
In case of BLUE, unbiased means the expected value of a mean estimate for an individual equals its true value. This is a conditional mean. By contrast, in case of BLUP the expected mean over all individuals is equal to the expected mean over all true effects.
Why BLUP is a good thing?
In animal breeding, Best Linear Unbiased Prediction, or BLUP, is a technique for estimating genetic merits. It can be used for removing noise from images and for small-area estimation.
What is meant by unbiased estimator?
An unbiased estimator of a parameter is an estimator whose expected value is equal to the parameter. That is, if the estimator S is being used to estimate a parameter θ, then S is an unbiased estimator of θ if E(S)=θ. Remember that expectation can be thought of as a long-run average value of a random variable.
Which is the best linear unbiased estimator to use?
Under assumptions V and VI, the OLS estimators are the best linear unbiased estimators (they are best in the sense of having minimum variance among all linear unbiased estimators), regardless of whether the ɛ i are normally distributed or not (Gauss–Markov theorem).
Which is the best definition of the BLUE estimator?
Definition of BLUE: Consider a data set whose parameterized PDF depends on the unknown parameter. 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
How is an estimate considered 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. Combining both the constraints (1) and (2) or (3),
Which is the best linear unbiased prediction in statistics?
Best linear unbiased prediction. In statistics, best linear unbiased prediction (BLUP) is used in linear mixed models for the estimation of random effects. BLUP was derived by Charles Roy Henderson in 1950 but the term best linear unbiased predictor (or prediction) seems not to have been used until 1962.