## 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

equal to the variance of every other unbiased

. . . , X9 denote a random sample from a distribution that is N(

ameter

**9**if Y is unbiased, that is, E( Y) =**9**, and if the variance of Y is less than orequal 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 327

first some unbiased estimator Y2 in their search for q>(Yx), an unbiased

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 Theorem3 simply convinces us that we can restrict our search for a best estimator to ...

Page 331

Let Z have a p.d.f. that is a member of the family {h(z;

- e-z'\ 0 < z < oo, = 0 elsewhere. ... Let the p.d.f. of Yt be gi(ji;

seen that, if there is any unbiased

Let Z have a p.d.f. that is a member of the family {h(z;

**9**):0<**9**<oo}, where A(z; 0) =- e-z'\ 0 < z < oo, = 0 elsewhere. ... Let the p.d.f. of Yt be gi(ji;

**9**),**9**e Q. It has beenseen that, if there is any unbiased

**estimator**Y2 (not a function of 7, alone) of**9**, ...### 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 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