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A Course in Mathematical Statistics and Large Sample Theory

A Course in Mathematical Statistics and Large Sample Theory

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  • ISBN:9781493940301
  • Editorial: Springer Verlag
  • Fecha de la edición:
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  • Nº Pág.:400
  • Idiomas:Ingles,Inglés

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This graduate-level textbook is primarily aimed at graduate students of statistics, mathematics, science, and engineering who have had an undergraduate course in statistics, an upper division course in analysis, and some acquaintance with measure theoretic probability. It provides a rigorous presentation of the core of mathematical statistics. Part I of this book constitutes a one-semester course on basic parametric mathematical statistics. Part II deals with the large sample theory of statistics - parametric and nonparametric, and its contents may be covered in one semester as well. Part III provides brief accounts of a number of topics of current interest for practitioners and other disciplines whose work involves statistical methods.

1 Introduction.- 2 Decision Theory.- 3 Introduction to General Methods of Estimation.- 4 Sufficient Statistics, Exponential Families, and Estimation.- 5 Testing Hypotheses.- 6 Consistency and Asymptotic Distributions and Statistics.- 7 Large Sample Theory of Estimation in Parametric Models.- 8 Tests in Parametric and Nonparametric Models.- 9 The Nonparametric Bootstrap.- 10 Nonparametric Curve Estimation.- 11 Edgeworth Expansions and the Bootstrap.- 12 Frechet Means and Nonparametric Inference on Non-Euclidean Geometric Spaces.- 13 Multiple Testing and the False Discovery Rate.- 14 Markov Chain Monte Carlo (MCMC) Simulation and Bayes Theory.- 15 Miscellaneous Topics.- Appendices.- Solutions of Selected Exercises in Part 1.

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