15 Point Estimators and Confidence Interval Flashcards
Estimator
A method for estimating the quantity of interest
Estimate
The value given by the estimator
What type of variable is an estimator
A random variable
What is point estimation
An estimation that gives one single answer
What is the criteria for assessing small sample estimators
Unbiasedness and efficiency
What is the criteria for assessing large sample estimators
Asymptotic unbiasedness and consistency
When is an estimator unbiased?
When the mean of its sampling distribution is equal to the parameter it is estimating
What is the bias of an estimator defined as?
The difference between its expected value and the value of the population parameter
What is an efficient estimator?
An estimator with a small variance, the smaller the variance the more efficient
Mean squared error
A combined measure of bias and inefficiency, the larger the value, the worse the estimate
When is an estimator asymptotically unbiased?
If as n becomes large, the bias tends to zero
When is an estimator consistent?
If the probability of observing an outcome from the sampling distribution of the estimator which is different to the population parameter becomes zero as n becomes very large
When will an asymptotically unbiased estimator be consistent?
When the variance of the estimator goes to 0 as n goes to infinity
When does an estimator with an infinite amount of sample information give a correct result?
When it is consistent
Confidence interval
An estimate that provides additional information about variability
