Statistical InferenceThis book builds theoretical statistics from the first principles of probability theory. Starting from the basics of probability, the authors develop the theory of statistical inference using techniques, definitions, and concepts that are statistical and are natural extensions and consequences of previous concepts. Intended for first-year graduate students, this book can be used for students majoring in statistics who have a solid mathematics background. It can also be used in a way that stresses the more practical uses of statistical theory, being more concerned with understanding basic statistical concepts and deriving reasonable statistical procedures for a variety of situations, and less concerned with formal optimality investigations. |
Contents
Probability Theory | 1 |
Transformations and Expectations | 50 |
Multiple Random Variables 139 | 140 |
Copyright | |
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acceptance ANOVA application approximation assume assumptions Bayes binomial bound calculate called Chapter complete compute conditional confidence confidence interval confidence set constant continuous converges defined Definition denote depend derived discussed distribution equal error Example Exercise exist expected experiment exponential expression fact Figure Find function given gives H₁ hence hypothesis independent Inequality inference integral interest interval joint known least Let X1 likelihood limit linear loss marginal mean measure method minimal normal Note observed obtain parameter particular Poisson population possible Principle probability problem proof properties prove random sample random variable region regression reject relationship result sample mean satisfies Show similar squares standard sufficient statistic Suppose Theorem transformation true Type unbiased estimator variance verify versus write