## 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 36

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

. . . , X9 denote a random sample from a distribution that is N(9, 1), — oo < 0 ...

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**For illustration, let Xu X2,. . . , X9 denote a random sample from a distribution that is N(9, 1), — oo < 0 ...

Page 326

For the adaptation in context of sufficient statistics, we let the sufficient statistic y,

be Xx and Y2, an unbiased statistic of 9, ... That is, through this conditioning, the

function (p(Yx) of the sufficient statistic y, is an

For the adaptation in context of sufficient statistics, we let the sufficient statistic y,

be Xx and Y2, an unbiased statistic of 9, ... That is, through this conditioning, the

function (p(Yx) of the sufficient statistic y, is an

**unbiased estimator**of 9 having ...Page 327

first some

of 9 based upon the sufficient statistic Yx . This is not the case at all, and 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 q>(Yx), an**unbiased estimator**of 9 based upon the sufficient statistic Yx . This is not the case at all, and Theorem

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 hypothesis H0 independent random variables integral joint p.d.f. Let the random Let Xu X2 limiting distribution marginal p.d.f. matrix moment-generating function order statistics p.d.f. of Xu 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 simple hypothesis statistic for 9 sufficient statistic testing H0 theorem unbiased estimator variance a2 Xx and X2 Yu Y2 zero elsewhere