## 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 262

The observed value of 0, n namely £ jc,-//i, is called the maximum likelihood

estimate of 9. For a simple i example, ... as a function of 9. When so regarded, it is

called the

The observed value of 0, n namely £ jc,-//i, is called the maximum likelihood

estimate of 9. For a simple i example, ... as a function of 9. When so regarded, it is

called the

**likelihood function**L of the random sample, and we write L(0; x„ x2t ...Page 264

This joint p.d.f., when regarded as a function of (0,, 92, . . . , 9m) eft, is called the

respect to 0,, 92, . . . , 9m, respectively, define the maximum likelihood estimators

0', ...

This joint p.d.f., when regarded as a function of (0,, 92, . . . , 9m) eft, is called the

**likelihood function**of the random ... that maximize this**likelihood function**withrespect to 0,, 92, . . . , 9m, respectively, define the maximum likelihood estimators

0', ...

Page 561

... 384 efficient, 377 maximum

square, 298 minimum mean-square-error ... 17

decision, 308, 433 distribution, 34, 37, 44, 78, 108, 501 gamma, 131

261,416 ...

... 384 efficient, 377 maximum

**likelihood**, 262, 324, 380, 385, 389 minimum chi-square, 298 minimum mean-square-error ... 17

**Function**, characteristic, 64decision, 308, 433 distribution, 34, 37, 44, 78, 108, 501 gamma, 131

**likelihood**,261,416 ...

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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