Question

distinguish between a point estimator and an estimate

Answer 1

Point Estimator:-

1) In statistics, point estimation involves the use of sample data to calculate a single value (known as a statistic) which is to serve as a "best guess" or "best estimate" of an unknown (fixed or random) population parameter.

2) A point estimate is the best estimate, in some sense, of the parameter based on a sample. It should be obvious that any point estimate is not absolutely accurate. It is an estimate based on only a single random sample. If repeated random samples were taken from the population, the point estimate would be expected to vary from sample to sample.

3) Point estimators are used to estimate population parameter. There are different variety of Point estimators as follows:-

a. Best Linear Unbaised Estimator(BLUE)

b. Maximum Likelihood Estimator(MLE)

c.Minimum Variance Unbaised Estimator(MVUE)

An Estimate:-

1) In statistics, an estimator is a rule for calculating an estimate of a given quantity based on observed data.

2) An estimator is a statistic that estimates some fact about the population. You can also think of an estimator as the rule that creates an estimate. For example, the sample mean(x̄) is an estimator for the population mean, μ.

3) The quantity that is being estimated (i.e. the one you want to know) is called the estimand. For example, let’s say you wanted to know the average height of children in a certain school with a population of 1000 students. You take a sample of 30 children, measure them and find that the mean height is 56 inches. This is your sample mean, the estimator. You use the sample mean to estimate that the population mean (your estimand) is about 56 inches.

4) Being a function of the data, the estimator is itself a random variable; a particular realization of this random variable is called the "estimate". Sometimes the words "estimator" and "estimate" are used interchangeably.