## Introduction to Mathematical StatisticsAn exceptionally clear and impeccably accurate presentation of statistical applications and more advanced theory. Included is a chapter on the distribution of functions of random variables as well as an excellent chapter on sufficient statistics. More modern technology is used in considering limiting distributions, making the presentations more clear and uniform. |

### From inside the book

Results 1-3 of 31

Page 308

ameter 9 if Y is unbiased, that is, E( Y) = 9, and if the variance of Y is less than or

equal to the variance of every other

Xu X2, . . . , X9 denote a random sample from a_ distribution that is N(9,\), — oo ...

ameter 9 if Y is unbiased, that is, E( Y) = 9, and if the variance of Y is less than or

equal to the variance of every other

**unbiased estimator**of 0. For illustration, letXu X2, . . . , X9 denote a random sample from a_ distribution that is N(9,\), — oo ...

Page 312

That is, 1 /Z is a

unbiased? It is interesting to note that if we maximize the two respective

likelihood ...

That is, 1 /Z is a

**biased estimator**while Y/ 1 0 is unbiased. Thus ,4 is using an**unbiased estimator**while B is not. Should we adjust B's estimator so that it too isunbiased? It is interesting to note that if we maximize the two respective

likelihood ...

Page 327

first some

Theorem 3 simply convinces us that we can restrict our search for a best

estimator to ...

first some

**unbiased estimator**Y2 in their search for <p( Yx ), an**unbiased****estimator**of 6 based upon the sufficient statistic F, . This is not the case at all, andTheorem 3 simply convinces us that we can restrict our search for a best

estimator to ...

### What people are saying - Write a review

We haven't found any reviews in the usual places.

### Other editions - View all

### Common terms and phrases

Accordingly approximate best critical region chi-square distribution complete sufficient statistic conditional p.d.f. conditional probability confidence interval Consider continuous type converges in probability correlation coefficient critical region defined degrees of freedom denote a random depend upon 9 discrete type distribution function F(x distribution with mean distribution with p.d.f. distribution with parameters equation estimator of 9 Example Exercise F-distribution gamma distribution given H0 is true independent random variables integral joint p.d.f. Let the random Let Xu X2 likelihood function limiting distribution marginal p.d.f. matrix moment-generating function order statistics p.d.f. of Yx percent confidence interval Poisson distribution positive integer probability density functions probability set function quadratic form random experiment random sample random variables Xx reject H0 respectively sample space Section Show significance level statistic for 9 subset testing H0 theorem u(Xu X2 unbiased estimator XuX2 Xx and X2 Yu Y2 zero elsewhere