Contents
What makes an estimator best estimator?
Point Estimates The point estimate is the single best value. A good estimator must satisfy three conditions: Consistent: The value of the estimator approaches the value of the parameter as the sample size increases. Relatively Efficient: The estimator has the smallest variance of all estimators which could be used.
How do you find the most efficient estimator?
Efficiency: The most efficient estimator among a group of unbiased estimators is the one with the smallest variance. For example, both the sample mean and the sample median are unbiased estimators of the mean of a normally distributed variable. However, X has the smallest variance.
What is the formula for finding out variance of estimates?
Assuming 0<σ2<∞, by definition σ2=E[(X−μ)2]. Thus, the variance itself is the mean of the random variable Y=(X−μ)2. This suggests the following estimator for the variance ˆσ2=1nn∑k=1(Xk−μ)2. However, in practice we often do not know the value of μ.
Why is the mean the best estimator?
We know the standard error of the mean is . Therefore in a normal distribution, the SE(median) is about 1.25 times . This is why the mean is a better estimator than the median when the data is normal (or approximately normal).
What are two traits of a good estimator?
Properties of Good Estimator
- Unbiasedness. An estimator is said to be unbiased if its expected value is identical with the population parameter being estimated.
- Consistency.
- Efficiency.
- Sufficiency.
Why is standard deviation a biased estimator?
Firstly, while the sample variance (using Bessel’s correction) is an unbiased estimator of the population variance, its square root, the sample standard deviation, is a biased estimate of the population standard deviation; because the square root is a concave function, the bias is downward, by Jensen’s inequality.