Asymptotic Statistics ― With a View to Stochastic Processes

Hopfner presents this volume of derivations of asymptotic statistics, with sections that also integrate stochastic processes but can be skipped to focus on statistics alone. The first chapter introduces basic material, defining score, information, and information bounds and discussing estimator sequences, asymptotics, heuristics, and consistency. Chapter two, standing in isolation, covers minimum distance estimators. The book then returns to foundations with chapters on contiguity and L2 differentiability. Core chapters 5-7 treat Gaussian shift models, mixed normal and quadratic models, and local asymptotics where one of the above is the limit model. The final chapter works with examples of stochastic process for LAN, LAMN, and LAQ type local asymptotics. An appendix presents further results of interest relating to stochastic processes, with many of the pertinent proofs relegated to references. Annotation c2014 Ringgold, Inc., Portland, OR (protoview.com)

Reinhard Hopfner, Johannes Gutenberg University Mainz, Germany.