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Advanced Statistics provides a rigorous development of statistics that emphasizes the definition and study of numerical measures that describe population variables. Volume 1 studies properties of commonly used descriptive measures. Volume 2 considers use of sampling from populations to draw inferences concerning properties of populations. The volumes are intended for use by graduate students in statistics and professional statisticians, although no specific prior knowledge of statistics is assumed. The rigorous treatment of statistical concepts requires that the reader be familiar with mathematical analysis and linear algebra, so that open sets, continuous functions, differentials, Raman integrals, matrices, and vectors are familiar terms.
1 Populations, Measurements, and Parameters.- 2 Expectations and Daniell Integrals.- 3 Random Variables and Measurable Functions.- 4 Construction of Daniell Integrals.- 5 Least Squares.- 6 Independence and Dependence.- 7 Quantiles.- 8 Moments.