## Introduction to Mathematical Statistics |

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Page 108

It should be noted that, although a statistic does not depend upon any unknown

that ...

It should be noted that, although a statistic does not depend upon any unknown

**parameter**, the distribution of that statistic may very well depend upon unknown**parameters**. Remark. We remark, for the benefit of the more advanced student,that ...

Page 205

Accordingly we define a “best” statistic for the

manner. Definition 2. For a given positive integer n, Yı = u1(X1, X2,..., Xn) will be

called a best statistic for the

variance ...

Accordingly we define a “best” statistic for the

**parameter**6 in the followingmanner. Definition 2. For a given positive integer n, Yı = u1(X1, X2,..., Xn) will be

called a best statistic for the

**parameter**6 if Yi is unbiased, E(Y) = 0, and if thevariance ...

Page 297

Let Q be the total

well represent several

Q. To test the hypothesis 0 e o, consider the subspaces ol, wa, ..., or 1 of Q, where

...

Let Q be the total

**parameter**space of the**parameter**6. The symbol 6 may verywell represent several

**parameters**; that is, 6 may be a vector. Let a be a subset ofQ. To test the hypothesis 0 e o, consider the subspaces ol, wa, ..., or 1 of Q, where

...

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accept accordance Accordingly alternative approximately assume called cent Chapter complete compute conditional confidence interval Consider constant continuous type critical region decision defined definition degrees of freedom denote a random depend determine discrete type distribution function equal Equation event Example EXERCISES exists expected fact given Hence inequality integral interval joint p.d.f. Let X1 likelihood marginal matrix maximum mean moment-generating function mutually stochastically independent normal distribution Note observed order statistics outcome parameter Pr(X probability density functions problem proof prove random experiment random interval random sample random variable ratio reject respectively result sample space Show significance level simple hypothesis ſº stochastically independent sufficient statistic symmetric matrix Table theorem transformation true unknown variance write X1 and X2 zero elsewhere