Re: estimator vs statistic
- From: Sheikh Ayoub <sheikhayoub@xxxxxxxxx>
- Date: Mon, 2 Feb 2009 10:08:40 -0800 (PST)
On Jan 30, 10:07 pm, AgEconomist <matttbog...@xxxxxxxxx> wrote:
On Jan 30, 8:38 am, Sheikh Ayoub <sheikhay...@xxxxxxxxx> wrote:
On Jan 30, 9:25 am, "David Jones" <dajx...@xxxxxxxxx> wrote:
Sheikh Ayoub wrote:
On Jan 30, 5:44 am, "David Jones" <dajx...@xxxxxxxxx> wrote:
Sheikh Ayoub wrote:
I'm going through the DeGroot book for self study and it can be
quite verbose at times and lose me. I'm on chapter 7 and baysesian
and MLE esitamators have already been introduced. Now statistics are
introduced which appear to be functions of observable random
variables broadly speaking. So here it seems that estimators are a
subset of statistics. Is this correct? Could anyone elaborate on the
distinction?
If you follow some people's terminology, an "estimator" is
essentially a rule for doing the calculations to create an
"estimate" or "statistic". The rule tells you what you would get for
the statistic if you were faced with samples other than the one you
have to hand, and often it would deal with a range of different
sample-sizes, not just a fixed size.
The distinction you make seems to be a fine distinction also in the
book. It seems like a statistic or sampling distribution of a
statistic is used prior to actually having observed data and helps to
inform you on what to expect. Whereas, an estimator is derived through
some method such as bayesian or MLE after observing some data. But
then it also goes on to say that you can workout an estimator without
plugging in the values and it would actually be a statistic as well..
So estimators are a subclass of statistic given them names and also
some methods to go about finding them. The terminology is a bit
confusing and the issue of whether values have been observed already
or not doesn't seem relevant to the distinction.
Chapter 7 is "Sampling Distributions of Estimators" and then goes on
to talk about Sampling Distributions of Statistics and or Estimators.
Also, for example, the bayseian estimate that minimizes the MSE for
sampling from a normal distribution is the sample mean. But the sample
mean is also a type of "statistic".
Perhaps I read too many philosophy books and not enough math books. I
would like the definitions to be a bit more tidy but it seems the book
is not providing that on this subject.
Well yes, people use these terms inconsistently.
The Oxford Dictionary of Statistical Terms says a statistic is "a summary value calculated from a sample of observations, usually but not necessarily as an estimator of some population parameter". The "not necesarily" may be important.
But another Dictionary of Statistics just says statistic is a function of the observations, whereas the one above empasizes the outcome value..
David Jones- Hide quoted text -
- Show quoted text -
I agree with your final remarks. That is the understanding I reached
after many tortuous hours with the Degroot book. I went through the
same thing, and refer back to it in my work from time to time. I read
it in conjuction with Goldberger's A course in Econometrics and
Kennedy's A Guide to Econometrics. Between the terminology and the
notation, I didn't think I was ever going to get through my first
semester of graduate school with that text. The lectures were just as
bad. In the end it was worth it. The foundation DeGroot provides is
quite valuable I believe.
I accept what you say. A statistic is a broad concept that can be
applied as estimators but not necessarily. I just have to be aware
that the terminology changes based on context and perspective. When
statistics are used to estimate parameters they are then refered to as
estimators.
I'm getting through the math ok but the terminology is continually
tripping me up. I think it has to do with the verbosity of the DeGroot
book(I liked the book overall).- Hide quoted text -
- Show quoted text -- Hide quoted text -
- Show quoted text -
Your post provides some encouragement. Thanks.
It can be frustrating but I also agree with you that DeGroot book has
lots of merit. He explains the theoretical groundwork in order for all
things to fit into their proper place whereas some of the other books
I've looked at don't provide that. Case in point: he starts with the
notion of estimators and some types of estimators and then goes on to
talk about sampling distributions of estimators. Other books seem to
introduce the sampling distribution of the mean and then move on to
estimators. Each topic seems to follow this pattern. He provides good
theoretical groundwork which motivates each topic. However, it
requires a lot more patience I'm not sure I have.
.
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