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 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 unbiased estimator of 0. For illustration, let
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, let
Xu X2, . . . , X9 denote a random sample from a_ distribution that is N(9,\), — oo ...
Page 327
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, 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 <p( Yx ), an unbiased
estimator of 6 based upon the sufficient statistic F, . This is not the case at all, and
Theorem 3 simply convinces us that we can restrict our search for a best
estimator to ...
Page 394
Robert V. Hogg. (a) Find the m.l.e., 6, of 9 and argue that it is a complete sufficient
statistic for 9. Is 9 unbiased? (b) If § is adjusted so that it is an unbiased estimator
of 9, what is a lower bound for the variance of this unbiased estimator? 8.29.
Robert V. Hogg. (a) Find the m.l.e., 6, of 9 and argue that it is a complete sufficient
statistic for 9. Is 9 unbiased? (b) If § is adjusted so that it is an unbiased estimator
of 9, what is a lower bound for the variance of this unbiased estimator? 8.29.
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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
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 | 27 Jan 2010 |
| ISBN | 0023557222, 9780023557224 |
| Length | 564 pages |
| Export Citation | BiBTeX EndNote RefMan |