I've been doing a little bit of research on this and i think the main difference between the two is that an estimator is function/formula/a process of calculations that give you an estimate( which is a final figure that expresses and is meant to equal a figure i.e population mean but does not actually equal it due to various errors in the given data/sample)
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I think, the estimate is a numerical value, wile the estimator is a function or operator, which can be generate more estimates according to some factors. For example (xbar) is estimator for (meu), which can be various when the sample size in various, the value that will be produced is an (estimate), but (xbar) is estimator.
An unbiased estimator is a person who gives a price for a service or goods and that person has no ulterior motives that would influence the price either way. A person who is biased might reflect the estimated price to show favor to one person more than another. For example: If my uncle was to bid on a job and I was the estimator for the person who wanted the work done, then I would have a bias in that I would reflect the price so that my uncle would get the job. This is unethical and illegal. An unbiased person has no preference as to who would get the job and would do the estimate honestly. An unbiased estimator has a very specific meaning in statistics and a good statistician needs to answer this meaning of the term.
Estimator is a noun that usually refers to the person or device doing the calculating or figuring. The estimate also can be used as a noun, referring to the result of a calculation or amount figured out, whether it be financial or area (i.e. furniture dimensions or price), it is the end result. However, estimate can also be used as the verb-the act of doing the calculating to come up with a certain amount or number.
Will a sample descriptive statistics accurately estimate the underlying population's parameters?
In the same way as you estimate them for whole numbers.