Point Estimate single, understood, efficient, concepts

atate2007

Hi guys, I havent quite understood these two concepts quite clearly... would appriciate it if you could shed some light...Thanks!

1)Are point estimates and sample statistics the same?

2) Schweser mentions that an unbiased estimator is efficient if the variance of the sampling distribution is smaller than that of all the other unbiased estimators of the parameter you are trying to estimate. .... How can a single parameter, say the mean, have multiple sampling distributions for each of the estimates... Doesn't a sample statistic have a single sample distribution?

koba

adq123 Wrote:
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> Hi guys, I havent quite understood these two
> concepts quite clearly... would appriciate it if
> you could shed some light...Thanks!
>
> 1)Are point estimates and sample statistics the
> same?
Point estimate means you are estimating a single variable. Sample statistics are just some properties of sample.
> 2) Schweser mentions that an unbiased estimator is
> efficient if the variance of the sampling
> distribution is smaller than that of all the other
> unbiased estimators of the parameter you are
> trying to estimate. .... How can a single
> parameter, say the mean, have multiple sampling
> distributions for each of the estimates... Doesn't
> a sample statistic have a single sample
> distribution?
For example, you can try to estimate expectation of a variable using a mean or a median. They are going to have different distributions. For example, if the variable is N(mu, sigma), then its mean = (x1+...+xN)/N is normally distributed N(mu, sigma/sqrt(N)) where N is the sample size.