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Spatial Aggregation of Local Likelihood Estimates with Applications to Classification

Spatial Aggregation of Local Likelihood Estimates with Applications to Classification
Author:
Publisher:
Total Pages:
Release: 2006
Genre:
ISBN:

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This paper presents a new method for spatially adaptive local likelihood estimation which applies to a broad class of nonparametric models, including the Gaussian, Poisson and binary response models. The main idea of the method is given a sequence of local likelihood estimates ("weak" estimates), to construct a new aggregated estimate whose pointwise risk is of order of the smallest risk among all "weak" estimates. We also propose a new approach towards selecting the parameters of the procedure by providing the prescribed behavior of the resulting estimate in the simple parametric situation. We establish a number of important theoretical results concerning the optimality of the aggregated estimate. In particular, our "oracle" results claims that its risk is up to some logarithmic multiplier equal to the smallest risk for the given family of estimates. The performance of the procedure is illustrated by application to the classification problem. A numerical study demonstrates its nice performance in simulated and real life examples. -- adaptive weights ; local likelihood ; exponential family ; classification


Applied Quantitative Finance

Applied Quantitative Finance
Author: Wolfgang Karl Härdle
Publisher: Springer Science & Business Media
Total Pages: 452
Release: 2008-08-26
Genre: Mathematics
ISBN: 3540691790

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Recent years have witnessed a growing importance of quantitative methods in both financial research and industry. This development requires the use of advanced techniques on a theoretical and applied level, especially when it comes to the quantification of risk and the valuation of modern financial products. Applied Quantitative Finance (2nd edition) provides a comprehensive and state-of-the-art treatment of cutting-edge topics and methods. It provides solutions to and presents theoretical developments in many practical problems such as risk management, pricing of credit derivatives, quantification of volatility and copula modelling. The synthesis of theory and practice supported by computational tools is reflected in the selection of topics as well as in a finely tuned balance of scientific contributions on practical implementation and theoretical concepts. This linkage between theory and practice offers theoreticians insights into considerations of applicability and, vice versa, provides practitioners comfortable access to new techniques in quantitative finance. Themes that are dominant in current research and which are presented in this book include among others the valuation of Collaterized Debt Obligations (CDOs), the high-frequency analysis of market liquidity, the pricing of Bermuda options and realized volatility. All Quantlets for the calculation of the given examples are downloadable from the Springer web pages.


The Annals of Statistics

The Annals of Statistics
Author:
Publisher:
Total Pages: 1012
Release: 2007
Genre: Mathematical statistics
ISBN:

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Local Neighborhood Transition Probability Estimation and Its Use in Contextual Classification

Local Neighborhood Transition Probability Estimation and Its Use in Contextual Classification
Author: National Aeronautics and Space Administration (NASA)
Publisher: Createspace Independent Publishing Platform
Total Pages: 34
Release: 2018-08-13
Genre:
ISBN: 9781725038523

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The problem of incorporating spatial or contextual information into classifications is considered. A simple model that describes the spatial dependencies between the neighboring pixels with a single parameter, Theta, is presented. Expressions are derived for updating the posteriori probabilities of the states of nature of the pattern under consideration using information from the neighboring patterns, both for spatially uniform context and for Markov dependencies in terms of Theta. Techniques for obtaining the optimal value of the parameter Theta as a maximum likelihood estimate from the local neighborhood of the pattern under consideration are developed. Chittineni, C. B. Unspecified Center NASA-CR-160261, LEC-13344, JSC-14859 NAS9-15800...


Local Likelihood Estimation

Local Likelihood Estimation
Author: Robert Tibshirani
Publisher: Ann Arbor, Mich. : University Microfilms International
Total Pages: 57
Release: 1984
Genre: Asymptotic efficiencies (Statistics)
ISBN:

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This paper extends the idea of local averaging to likelihood based models. One such application is to the class of generalized linear models. The author enlarges this class by replacing the covariate from chi beta with an unspecified smooth function. This function is estimated from the data by a technique called Local Likelihood Estimation - a type of local averaging. Multiple covariates are incorporated through a forward stepwise algorithm. The main application discussed however, is to the proportional hazards model of Cox (1972), for censored data, In a number of real data examples, the local likelihood technique proves to be effective in uncovering non-linear dependencies. Finally, the author gives some asymptotic results for local likelihood estimates and provides some methods for inference.


Theory of Spatial Statistics

Theory of Spatial Statistics
Author: M.N.M. van Lieshout
Publisher: CRC Press
Total Pages: 162
Release: 2019-03-19
Genre: Mathematics
ISBN: 0429627033

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Theory of Spatial Statistics: A Concise Introduction presents the most important models used in spatial statistics, including random fields and point processes, from a rigorous mathematical point of view and shows how to carry out statistical inference. It contains full proofs, real-life examples and theoretical exercises. Solutions to the latter are available in an appendix. Assuming maturity in probability and statistics, these concise lecture notes are self-contained and cover enough material for a semester course. They may also serve as a reference book for researchers. Features * Presents the mathematical foundations of spatial statistics. * Contains worked examples from mining, disease mapping, forestry, soil and environmental science, and criminology. * Gives pointers to the literature to facilitate further study. * Provides example code in R to encourage the student to experiment. * Offers exercises and their solutions to test and deepen understanding. The book is suitable for postgraduate and advanced undergraduate students in mathematics and statistics.


geoENV IV — Geostatistics for Environmental Applications

geoENV IV — Geostatistics for Environmental Applications
Author: Xavier Sanchez-Vila
Publisher: Springer Science & Business Media
Total Pages: 550
Release: 2006-04-11
Genre: Science
ISBN: 1402021151

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The fourth edition of the European Conference on Geostatistics for Environmental Applications (geoENV IV) took place in Barcelona, November 27-29, 2002. As a proof that there is an increasing interest in environmental issues in the geostatistical community, the conference attracted over 100 participants, mostly Europeans (up to 10 European countries were represented), but also from other countries in the world. Only 46 contributions, selected out of around 100 submitted papers, were invited to be presented orally during the conference. Additionally 30 authors were invited to present their work in poster format during a special session. All oral and poster contributors were invited to submit their work to be considered for publication in this Kluwer series. All papers underwent a reviewing process, which consisted on two reviewers for oral presentations and one reviewer for posters. The book opens with one keynote paper by Philippe Naveau. It is followed by 40 papers that correspond to those presented orally during the conference and accepted by the reviewers. These papers are classified according to their main topic. The list of topics show the diversity of the contributions and the fields of application. At the end of the book, summaries of up to 19 poster presentations are added. The geoENV conferences stress two issues, namely geostatistics and environmental applications. Thus, papers can be classified into two groups.


Spatial Analysis in Epidemiology

Spatial Analysis in Epidemiology
Author: Dirk Pfeiffer
Publisher: Oxford University Press
Total Pages: 171
Release: 2008-05-29
Genre: Computers
ISBN: 019850988X

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Providing a practical, comprehensive and up-to-date overview of the use of spatial statistics in epidemiology, this book examines spatial analytical methods in conjunction with GIS and remotely sensed data to provide insights into the patterns and processes that underlie disease transmission.


geoENV VI – Geostatistics for Environmental Applications

geoENV VI – Geostatistics for Environmental Applications
Author: Amílcar Soares
Publisher: Springer Science & Business Media
Total Pages: 500
Release: 2008-03-12
Genre: Science
ISBN: 1402064489

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This volume contains 40 selected full-text contributions from the Sixth European Conference on Geostatistics for Environmental Applications, geoENV IV, held in Rhodes, Greece, October 25-26, 2006. The objective of the editors was to compile a set of papers from which the reader could perceive how geostatistics is applied within the environmental sciences. A few selected theoretical contributions are also included.