Introduction to Mathematical Statistics |
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Page 210
... sufficient statistic for 0. The joint p.d.f. of Y1 , Y2 , Yз , Y is 4 4 g ( Y1 , Y2 , Y3 , Y4 ; 0 ) 4 ! = 04 ' 0 < Y1 < Y2 < Y3 < Y4 < 0 , = 0 elsewhere ... Sufficient Statistics [ Ch . 8 Criteria for the Existence of a Sufficient Statistic.
... sufficient statistic for 0. The joint p.d.f. of Y1 , Y2 , Yз , Y is 4 4 g ( Y1 , Y2 , Y3 , Y4 ; 0 ) 4 ! = 04 ' 0 < Y1 < Y2 < Y3 < Y4 < 0 , = 0 elsewhere ... Sufficient Statistics [ Ch . 8 Criteria for the Existence of a Sufficient Statistic.
Page 215
... statistic for a parameter 0 , let us consider an important property possessed by a sufficient statistic Y1 u1 ( X1 , X2 , . . . , Xn ) for 0. The conditional p.d.f. of another statistic , say , Y2 u2 ( X1 , X2 , . . . , Xn ) , given Y1 ...
... statistic for a parameter 0 , let us consider an important property possessed by a sufficient statistic Y1 u1 ( X1 , X2 , . . . , Xn ) for 0. The conditional p.d.f. of another statistic , say , Y2 u2 ( X1 , X2 , . . . , Xn ) , given Y1 ...
Page 218
... sufficient statistic for the parameter 0. Let Y2 = u2 ( X1 , X2 , ... , Xn ) be another statistic ( but not a function of Y1 alone ) which is an unbiased statistic for 0 ; that is ... sufficient statistic 218 Sufficient Statistics [ Ch . 8.
... sufficient statistic for the parameter 0. Let Y2 = u2 ( X1 , X2 , ... , Xn ) be another statistic ( but not a function of Y1 alone ) which is an unbiased statistic for 0 ; that is ... sufficient statistic 218 Sufficient Statistics [ Ch . 8.
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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