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
... 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 estimator of 0 ; that definition requires that the comparison be made with every ...
... 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 estimator of 0 ; that definition requires that the comparison be made with every ...
Page 327
... estimator of based upon the sufficient statistic Y ,. This is not the case at all , and Theorem 3 simply convinces us that we can restrict our search for a best estimator ... [ 9 ( Y1 ) | Y3 = y3 ] , where Y is another statistic , which is not ...
... estimator of based upon the sufficient statistic Y ,. This is not the case at all , and Theorem 3 simply convinces us that we can restrict our search for a best estimator ... [ 9 ( Y1 ) | Y3 = y3 ] , where Y is another statistic , which is not ...
Page 387
... 9 where is some preliminary estimator of 0 , like the Sec . 8.4 ] Robust M - Estimation 387 Robust M-Estimation.
... 9 where is some preliminary estimator of 0 , like the Sec . 8.4 ] Robust M - Estimation 387 Robust M-Estimation.
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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 Find the p.d.f. 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 subset sufficient statistic t-distribution t₂ theorem unbiased estimator variance o² X₁ X₂ Y₁ Y₂ zero elsewhere μ₁ σ²