## 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. |

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Page 318

Since this ratio does not

Example 3. Let Yx < Y2 < . . . < Y„ denote the order statistics of a random sample

of size n from the distribution with p.d.f. Here we use the indicator function of set A

...

Since this ratio does not

**depend upon 9**, the sum Yx is a sufficient statistic for 9.Example 3. Let Yx < Y2 < . . . < Y„ denote the order statistics of a random sample

of size n from the distribution with p.d.f. Here we use the indicator function of set A

...

Page 350

0, for all 9. That is, there is a nonzero function of those minimal sufficient statistics,

Yx and Y„, whose expectation is zero for ... S2 of a random sample from N(9, 1)

has a distribution that does not

0, for all 9. That is, there is a nonzero function of those minimal sufficient statistics,

Yx and Y„, whose expectation is zero for ... S2 of a random sample from N(9, 1)

has a distribution that does not

**depend upon 9**and hence is an ancillary statistic.Page 353

7.9 Sufficiency, Completeness, and Independence We have noted that if we have

a sufficient statistic F, for a parameter 9, 9eQ, then h(z\yx), the conditional p.d.f. of

another statistic Z, given F, = yx , does not

7.9 Sufficiency, Completeness, and Independence We have noted that if we have

a sufficient statistic F, for a parameter 9, 9eQ, then h(z\yx), the conditional p.d.f. of

another statistic Z, given F, = yx , does not

**depend upon 9**. If, moreover, Y\ and ...### What people are saying - Write a review

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### 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