## Introduction to mathematical statistics |

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Page 249

That is, one of these

9 and the other

had restricted our consideration to

all ...

That is, one of these

**decision functions**is better than the other for some values of9 and the other

**decision function**is better for other values of 9. If, however, wehad restricted our consideration to

**decision functions**w such that E[w(Y)] = 8 forall ...

Page 250

If we restrict our considerations to

where b does not depend upon y, show that R(8, w) = b2 + 9/n. What

If we restrict our considerations to

**decision functions**of the form w(y) = b + y/n,where b does not depend upon y, show that R(8, w) = b2 + 9/n. What

**decision****function**of this form yields a uniformly smaller risk than every other**decision****function**...Page 279

procedures (in particular, minimax decisions) and Bayesian procedures. In this

section, we apply these ... is Q = [8; 8 = 8', 8"}. In accordance with the

or, ...

procedures (in particular, minimax decisions) and Bayesian procedures. In this

section, we apply these ... is Q = [8; 8 = 8', 8"}. In accordance with the

**decision****function**procedure, we need a function w of the observed values ot X1, . . . , Xn (or, ...

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### Common terms and phrases

Accordingly best critical region binomial distribution cent confidence interval Chapter chi-square distribution complete sufficient statistic conditional p.d.f. confidence interval Consider continuous type converges stochastically critical region decision function defined degrees of freedom denote a random discrete type distribution having p.d.f. Equation Example EXERCISES F distribution function of Y1 given H0 is true independent random variables inequality integral joint p.d.f. Let the random Let X1 limiting distribution marginal p.d.f. matrix maximum likelihood moment-generating function mutually stochastically independent noncentral order statistics Poisson distribution positive integer power function Pr X1 probability density functions probability set function quadratic form random experiment random interval random sample random variables X1 reject H0 respectively sample space Show significance level simple hypothesis H0 statistic for 9 statistic Y1 stochastically independent random subset testing H0 theorem type of random unbiased statistic variance a2 X1 and X2 Xn denote zero elsewhere