The Advanced Theory of Statistics, Volume 2

a₁ alog alternative approximation asymptotic variance asymptotically normally binomial Biometrika bivariate normal C. R. Rao Chapter confidence intervals consider correlation coefficient critical region defined degrees of freedom deviation discussed dispersion matrix distribution-free E. S. Pearson efficiency equal equation error Example Exercise fixed frequencies given gives H₁ Hence holds hypothesis independent large samples Likelihood Likelihood Function LR test method minimal ML estimator multinomial distribution n₁ n₂ non-central normal distribution normal population observations obtain order-statistics orthogonal parameters Poisson distribution power function probability problem random variables ratio regression result sample mean single sufficient statistic Student's sufficient statistic t₁ t₂ test statistic theory tion UMPU tests unbiassed estimator variate vector write x₁ xª distribution zero θο μ₁ μο σ² σι