Introduction to Mathematical Statistics |
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Page 208
... statistic " can be explained as follows : If a statistic Y1 satisfies the preceding definition , then the conditional p.d.f. of Y2 , say , given Y1 y1 , does not depend upon the parameter 0. As a consequence , once given Y1 = y1 , it is ...
... statistic " can be explained as follows : If a statistic Y1 satisfies the preceding definition , then the conditional p.d.f. of Y2 , say , given Y1 y1 , does not depend upon the parameter 0. As a consequence , once given Y1 = y1 , it is ...
Page 218
... y1 ) . This expectation is a function of y1 , say , ( y1 ) . Since Y1 is a sufficient statistic for 0 , the conditional p.d.f. of Y2 , given Yı = y1 , does not depend upon so that E ( Y2 | y1 ) = q ( Y1 ) is a function of y1 alone ...
... y1 ) . This expectation is a function of y1 , say , ( y1 ) . Since Y1 is a sufficient statistic for 0 , the conditional p.d.f. of Y2 , given Yı = y1 , does not depend upon so that E ( Y2 | y1 ) = q ( Y1 ) is a function of y1 alone ...
Page 222
Robert V. Hogg, Allen Thornton Craig. E [ p ( Y1 ) ] = 0 for all values of 0 , 0 = N. Let 1 ( Y1 ) be another continuous function of the sufficient statistic Y1 alone so that we have also E [ ( Y1 ) ] = 0 for all values of 0 , 0 e Q. Hence ...
Robert V. Hogg, Allen Thornton Craig. E [ p ( Y1 ) ] = 0 for all values of 0 , 0 = N. Let 1 ( Y1 ) be another continuous function of the sufficient statistic Y1 alone so that we have also E [ ( Y1 ) ] = 0 for all values of 0 , 0 e Q. Hence ...
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A₁ A₂ accept accordance Accordingly alternative approximately assume called cent Chapter complete compute 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 H₁ Hence hypothesis 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 parameter 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 stochastically independent sufficient statistic symmetric matrix Table theorem transformation true unknown variables X1 variance W₁ X₁ X₂ Y₁ Y₂ zero elsewhere μ₁