Introduction to Mathematical StatisticsThe fifth edition of text offers a careful presentation of the probability needed for mathematical statistics and the mathematics of statistical inference. Offering a background for those who wish to go on to study statistical applications or more advanced theory, this text presents a thorough treatment of the mathematics of statistics. |
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Page 308
... unbiased estimator of 0. The statistic X , is N ( 0 , 1 ) , so X , is also an unbiased estimator of 0. Although the variance of X is less than the variance 1 of X1 , we cannot say , with n = 9 , that X is the unbiased minimum variance ...
... unbiased estimator of 0. The statistic X , is N ( 0 , 1 ) , so X , is also an unbiased estimator of 0. Although the variance of X is less than the variance 1 of X1 , we cannot say , with n = 9 , that X is the unbiased minimum variance ...
Page 327
Robert V. Hogg, Allen Thornton Craig. first some unbiased estimator Y2 in their search for ø ( Y1 ) , an unbiased estimator of based upon the sufficient statistic Y1 . This is not the case at all , and Theorem 3 simply convinces us that ...
Robert V. Hogg, Allen Thornton Craig. first some unbiased estimator Y2 in their search for ø ( Y1 ) , an unbiased estimator of based upon the sufficient statistic Y1 . This is not the case at all , and Theorem 3 simply convinces us that ...
Page 340
... estimator of e - 20 that is unbiased and has minimum variance . Consider Y = ( -1 ) . We have -20 ∞ ( -0 ) * e - 0 = x ! E ( Y ) = E [ ( − 1 ) 3 ] = Σ x = 0 Accordingly , ( -1 ) * is the unbiased minimum variance estimator of e - 20 ...
... estimator of e - 20 that is unbiased and has minimum variance . Consider Y = ( -1 ) . We have -20 ∞ ( -0 ) * e - 0 = x ! E ( Y ) = E [ ( − 1 ) 3 ] = Σ x = 0 Accordingly , ( -1 ) * is the unbiased minimum variance estimator of e - 20 ...
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A₁ A₂ Accordingly approximate best critical region C₁ C₂ chi-square distribution complete sufficient statistic conditional p.d.f. confidence interval Consider continuous type converges in probability correlation coefficient critical region defined degrees of freedom denote a random discrete type distribution function F(x distribution with mean distribution with p.d.f. distribution with parameters dx₁ equation Example Exercise g₁(y₁ gamma distribution given H₁ Hint hypothesis H independent random variables integral Let the random Let X1 Let Y₁ limiting distribution marginal p.d.f. matrix mean µ moment-generating function order statistics p.d.f. of Y₁ P(C₁ p₁ percent confidence interval Poisson distribution positive integer probability density functions probability set function r₁ random experiment random sample respectively sample space Section Show significance level simple hypothesis sufficient statistic t-distribution t₂ theorem unbiased estimator variance o² X₁ X₂ Y₁ Y₂ zero elsewhere μ₁ Σ Σ σ²