Unit 6 Flashcards
What is an estimator?
A formula/function for obtaining an estimate once the data are known
2 types of estimates?
Point or interval
What do we need to consider to tell if an estimator is a best estimator?
Location (is it biased?)
Dispersion
What does bias find out?
Whether Θ>θ or Θ
Why is the mean squared error a better measure usually than variance for measuring dispersion?
Var(θ) works as dispersion measure if the estimator is unbiased, but to allow for possibility of bias it is better to use MSE
What does the MSE measure?
The average squared distance of θ(hat) from θ
What is the standard error and why do we use it?
It is the route of the MSE, and use it since MSE is a bit melodramatic
What is a consistent estimator?
An estimator such that as its’ sample size increases, the MSE tends to 0
What is an efficient estimator?
An estimator is said to be efficient if it can be shown NO estimator has a lower MSE at any sample size
See
Page 8 notes on relative efficiency
What is an asymptotically efficient estimator?
An estimator is asymptotically efficient if it’s MSE RELATIVE TO some other estimator tends to <=1 as N->infinity (even though it isn’t efficient)
What to do when you’re stuck trying to find variance?
Check if the variable has a Bernoulli distribution! If it does use:
Var(X)=p(1-p)/n
