Non linearity arises in statistical inference in various ways, with varying degrees of severity, as an obstacle to statistical analysis. More entrenched forms of nonlinearity often require intensive numerical methods to construct estimators, and the use of root search algorithms, or one-step estimators, is a standard method of solution. This book provides a comprehensive study of nonlinear estimating equations and artificial likelihood's for statistical inference. It provides extensive coverage and comparison of hill climbing algorithms, which when started at points of nonconcavity often have very poor convergence properties, and for additional flexibility proposes a number of modification to the standard methods for solving these algorithms. The book also extends beyond simple root search algorithms to include a discussion of the testing of roots for consistency, and the modification of available estimating functions to provide greater stability in inference. A variety of examples from practical applications are included to illustrate the problems and possibilities thus making this text ideal for the research statistician and graduate student.
Many books have been written on the theory of functional equations, but very few help readers solve functional equations in mathematics competitions and mathematical problem solving. This book fills that gap. Each chapter includes a list of problems associated with the covered material. These vary in difficulty, with the easiest being accessible to any high school student who has read the chapter carefully. The most difficult will challenge students studying for the International Mathematical Olympiad or the Putnam Competition. An appendix provides a springboard for further investigation of the concepts of limits, infinite series and continuity.
Explains how Hilbert space techniques cross the boundaries into the foundations of probability and statistics. Focuses on the theory of martingales stochastic integration, interpolation and density estimation. Includes a copious amount of problems and examples.
Asymptotic methods provide important tools for approximating and analysing functions that arise in probability and statistics. Moreover, the conclusions of asymptotic analysis often supplement the conclusions obtained by numerical methods. Providing a broad toolkit of analytical methods, Expansions and Asymptotics for Statistics shows how asymptoti
Asymptotic methods provide important tools for approximating and analysing functions that arise in probability and statistics. Moreover, the conclusions of asymptotic analysis often supplement the conclusions obtained by numerical methods. Providing a broad toolkit of analytical methods, Expansions and Asymptotics for Statistics shows how asymptoti
In general terms, the shape of an object, data set, or image can be de fined as the total of all information that is invariant under translations, rotations, and isotropic rescalings. Thus two objects can be said to have the same shape if they are similar in the sense of Euclidean geometry. For example, all equilateral triangles have the same shape, and so do all cubes. In applications, bodies rarely have exactly the same shape within measure ment error. In such cases the variation in shape can often be the subject of statistical analysis. The last decade has seen a considerable growth in interest in the statis tical theory of shape. This has been the result of a synthesis of a number of different areas and a recognition that there is considerable common ground among these areas in their study of shape variation. Despite this synthesis of disciplines, there are several different schools of statistical shape analysis. One of these, the Kendall school of shape analysis, uses a variety of mathe matical tools from differential geometry and probability, and is the subject of this book. The book does not assume a particularly strong background by the reader in these subjects, and so a brief introduction is provided to each of these topics. Anyone who is unfamiliar with this material is advised to consult a more complete reference. As the literature on these subjects is vast, the introductory sections can be used as a brief guide to the literature.
This volume helps designers to recognize and identify typefaces seen and used on an everyday basis, and also provides assistance with the process of typeface selection. It highlights the essential characteristics of over 700 typeface specimens.
To ensure that you have the most up-to-date and complete materials for your Environmental Law class, be sure to use Environmental Regulation: Statutory and Case Supplement with Internet Guide, 2008-2009 Edition . ENVIRONMENTAL JUSTICE Title VI of the Civil Rights Act of 1964 U.S. Environmental Protection Agency Title VI Regulations Executive Order 12,898, Environmental Justice THE REGULATORY PROCESS Administrative Procedure Act; Regulatory Flexibility Act Information Quality Act and OMB Guidelines Congressional Review Act Regulatory Planning and Review, Executive Order 12,866 REGULATION OF TOXIC SUBSTANCES Toxic Substances Control Act Federal Insecticide, Fungicide, and Rodenticide Act Safe Drinking Water Act Emergency Planning and Community Right-to-Know Act Safe Drinking Water and Toxic Enforcement Act (Proposition 65) WASTE MANAGEMENT AND POLLUTION PREVENTION Solid Waste Disposal Act (as Amended by the Resource Conservation and Recovery Act) Comprehensive Environmental Response, Compensation, and Liability Act Pollution Prevention Act AIR POLLUTION CONTROL Clean Air Act WATER POLLUTION CONTROL Federal Water Pollution Control Act (Clean Water Act) Oil Pollution Act LAND USE REGULATION Coastal Zone Management Act ENVIRONMENTAL ASSESSMENT National Environmental Policy Act NEPA Regulations BIODIVERSITY PROTECTION Endangered Species Act PUBLIC LAND MANAGEMENT Antiquities Act; Multiple Use Sustained Yield Act Forest and Rangeland Renewable Resources Planning Act Federal Land Policy and Management Act CASE SUPPLEMENT United States v. Atlantic Research Corp. United Haulers Assn., Inc. v. Oneida-Herkimer Solid Waste Management Authority Environmental Defense v. Duke Energy Corp. Massachusetts v. EP Rapanos v. United States S.D. Warren Co. v. Maine Board of Environmental Protection Exxon Shipping Company v. Baker National Assn. Of Homebuilders v. Defenders of Wildlife
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