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- What is the relation between estimator and estimate?
In Lehmann's formulation, almost any formula can be an estimator of almost any property There is no inherent mathematical link between an estimator and an estimand However, we can assess--in advance--the chance that an estimator will be reasonably close to the quantity it is intended to estimate
- What is the difference between a consistent estimator and an unbiased . . .
An estimator is unbiased if, on average, it hits the true parameter value That is, the mean of the sampling distribution of the estimator is equal to the true parameter value
- Prove that the OLS estimator of the intercept is BLUE
This is one of those theorems that is easier to prove in greater generality using vector algebra than it is to prove with scalar algebra To do this, consider the multiple linear regression model and consider the general linear estimator: Since the OLS estimator is unbiased and this general linear estimator has bias: and so the requirement of unbiasedness imposes the restriction that The
- What is the difference between estimation and prediction?
purpose: an estimator seeks to know a property of the true state of nature, while a prediction seeks to guess the outcome of a random variable; and uncertainty: a predictor usually has larger uncertainty than a related estimator, due to the added uncertainty in the outcome of that random variable Well-documented and -described predictors therefore usually come with uncertainty bands
- When is a biased estimator preferable to unbiased one?
It's obvious many times why one prefers an unbiased estimator But, are there any circumstances under which we might actually prefer a biased estimator over an unbiased one?
- When is a maximum likelihood estimator biased? [duplicate]
It is known that maximum likelihood estimators (MLE) can be biased Can we predict whether a given distribution and parameter of interest will produce a biased MLE? On what properties does it depend?
- How to derive the least square estimator for multiple linear regression . . .
How to derive the least square estimator for multiple linear regression? Ask Question Asked 13 years, 3 months ago Modified 3 years, 4 months ago
- How to prove $s^2$ is a consistent estimator of $\sigma^2$?
How to prove $s^2$ is a consistent estimator of $\sigma^2$? Ask Question Asked 5 years, 4 months ago Modified 2 years, 3 months ago
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