Introduction to Mathematical Statistics |
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Page 248
... decision function or a decision rule . One value of the decision function , say w ( y ) , is called a decision . Thus a numerically determined point estimate of a parameter 0 is a decision . Now a decision may be correct or it may be ...
... decision function or a decision rule . One value of the decision function , say w ( y ) , is called a decision . Thus a numerically determined point estimate of a parameter 0 is a decision . Now a decision may be correct or it may be ...
Page 249
... decision functions is better than the other for some values of and the other decision function is better for other values of 0 . If , however , we had restricted our consideration to decision functions w such that E [ w ( Y ) ] = 0 for ...
... decision functions is better than the other for some values of and the other decision function is better for other values of 0 . If , however , we had restricted our consideration to decision functions w such that E [ w ( Y ) ] = 0 for ...
Page 250
... decision functions of the form w ( y ) = b + y / n , where b does not depend upon y , show that R ( 0 , w ) = b2 + 0 / n . What decision function of this form yields a uniformly smaller risk than every other decision function of this ...
... decision functions of the form w ( y ) = b + y / n , where b does not depend upon y , show that R ( 0 , w ) = b2 + 0 / n . What decision function of this form yields a uniformly smaller risk than every other decision function of this ...
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A₁ A₂ Accordingly best critical region c₁ cent confidence interval chi-square distribution complete sufficient statistic compute conditional p.d.f. confidence interval Consider continuous type critical region decision function defined degrees of freedom denote a random discrete type distribution function distribution having p.d.f. Equation Example EXERCISES function F(x given H₁ hypothesis H independent random variables integral joint p.d.f. k₁ Let X1 Let Y₁ limiting distribution marginal p.d.f. matrix maximum likelihood moment-generating function mutually stochastically independent noncentral normal distribution order statistics p.d.f. of Y₁ P(A₁ p₁ Poisson distribution positive integer probability density functions quadratic form random experiment random interval random sample random variables X1 respectively sample space Show significance level simple hypothesis statistic Y₁ stochastically independent random sufficient statistic theorem unbiased statistic variance o² w₁ X₁ X₁ and X2 X₂ Y₂ Z₁ zero elsewhere μ₁ μ₂ Σ Σ