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 322
7.3 Properties of a Sufficient Statistic Suppose that a random sample Xu X2, . . . ,
X„ is taken from a distribution with p.d.f. f(x; 9) that depends upon one parameter
9 e Q. Say that a sufficient statistic Yx = ux(Xu X2, . . . , X„) for 9 exists and has ...
7.3 Properties of a Sufficient Statistic Suppose that a random sample Xu X2, . . . ,
X„ is taken from a distribution with p.d.f. f(x; 9) that depends upon one parameter
9 e Q. Say that a sufficient statistic Yx = ux(Xu X2, . . . , X„) for 9 exists and has ...
Page 353
7.9 Sufficiency, Completeness, and Independence We have noted that if we have
a sufficient statistic Yx for a parameter 6, 0eCl, then h(z\yt), the conditional p.d.f. of
another statistic Z, given Yx = yx , does not depend upon 9. If, moreover, Yx ...
7.9 Sufficiency, Completeness, and Independence We have noted that if we have
a sufficient statistic Yx for a parameter 6, 0eCl, then h(z\yt), the conditional p.d.f. of
another statistic Z, given Yx = yx , does not depend upon 9. If, moreover, Yx ...
Page 354
e °f probability density functions of Yx be complete. Let Z = u(X, , X2, . . . , X„) be
any other statistic (not a function of Yx alone). If the distribution of Z does not
depend upon 9, then Z is independent of the sufficient statistic Yx . In the
discussion ...
e °f probability density functions of Yx be complete. Let Z = u(X, , X2, . . . , X„) be
any other statistic (not a function of Yx alone). If the distribution of Z does not
depend upon 9, then Z is independent of the sufficient statistic Yx . In the
discussion ...
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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 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
Bibliographic information
| Title | Introduction to Mathematical Statistics Prentice Hall International Editions |
| Author | Robert V. Hogg |
| Contributor | Allen Thornton Craig |
| Edition | 5, illustrated |
| Publisher | Prentice Hall, 1995 |
| Original from | the University of Michigan |
| Digitized | 3 Feb 2010 |
| ISBN | 0023557222, 9780023557224 |
| Length | 564 pages |
| Export Citation | BiBTeX EndNote RefMan |