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The Universality of the Radon Transform

Leon Ehrenpreis

Published in print:
2003
Published Online:
September 2007
ISBN:
9780198509783
eISBN:
9780191709166
Item type:
book
Publisher:
Oxford University Press
DOI:
10.1093/acprof:oso/9780198509783.001.0001
Subject:
Mathematics, Mathematical Physics

Radon showed how to write arbitrary functions in Rn in terms of the characteristic functions (delta functions) of hyperplanes. This idea leads to various generalizations. For example, R can be ... More


INTRODUCTION

Leon Ehrenpreis

in The Universality of the Radon Transform

Published in print:
2003
Published Online:
September 2007
ISBN:
9780198509783
eISBN:
9780191709166
Item type:
chapter
Publisher:
Oxford University Press
DOI:
10.1093/acprof:oso/9780198509783.003.0001
Subject:
Mathematics, Mathematical Physics

This introductory chapter presents a detailed summary of the highlights of the book. In particular, it explains in various contexts why the Radon transform leads to a “basis” for all functions, and ... More


Statistical Alternatives and Supplements to Random Sampling

Patrick Dattalo

in Strategies to Approximate Random Sampling and Assignment

Published in print:
2009
Published Online:
February 2010
ISBN:
9780195378351
eISBN:
9780199864645
Item type:
chapter
Publisher:
Oxford University Press
DOI:
10.1093/acprof:oso/9780195378351.003.0003
Subject:
Social Work, Research and Evaluation

This chapter describes the following alternatives and complements to RS in terms of their assumptions, implementations, strengths, and weaknesses: (1) randomization tests; (2) multiple imputation; ... More


Statistical Inference in Nonparametric Frontier Models: Recent Developments and Perspectives

Léopold Simar Paul W. Wilson

in The Measurement of Productive Efficiency and Productivity Change

Published in print:
2008
Published Online:
January 2008
ISBN:
9780195183528
eISBN:
9780199870288
Item type:
chapter
Publisher:
Oxford University Press
DOI:
10.1093/acprof:oso/9780195183528.003.0004
Subject:
Economics and Finance, Econometrics

This chapter recasts the parametric and statistical approach of Chapter 2, and the nonparametric and deterministic approach of Chapter 3 into a nonparametric and statistical approach. It presents in ... More


Human Capital and Economic Growth

Andreas Savvides and Thanasis Stengos

Published in print:
2008
Published Online:
June 2013
ISBN:
9780804755405
eISBN:
9780804769761
Item type:
book
Publisher:
Stanford University Press
DOI:
10.11126/stanford/9780804755405.001.0001
Subject:
Economics and Finance, Econometrics

This book provides an in-depth investigation of the link between human capital and economic growth. The book examines the determinants of economic growth through a historical overview of the concept ... More


Nonparametric Bayesian Networks *

Katja Ickstadt, Bjöorn Bornkamp, Marco Grzegorczyk, Jakob Wieczorek, Malik R. Sheriff, Hernáan E. Grecco, and Eli Zamir

in Bayesian Statistics 9

Published in print:
2011
Published Online:
January 2012
ISBN:
9780199694587
eISBN:
9780191731921
Item type:
chapter
Publisher:
Oxford University Press
DOI:
10.1093/acprof:oso/9780199694587.003.0010
Subject:
Mathematics, Probability / Statistics

A convenient way of modelling complex interactions is by employing graphs or networks which correspond to conditional independence structures in an underlying statistical model. One main class of ... More


Particle Learning for Sequential Bayesian Computation *

Hedibert F. Lopes, Michael S. Johannes, Carlos M. Carvalho, and Nicholas G. Polson

in Bayesian Statistics 9

Published in print:
2011
Published Online:
January 2012
ISBN:
9780199694587
eISBN:
9780191731921
Item type:
chapter
Publisher:
Oxford University Press
DOI:
10.1093/acprof:oso/9780199694587.003.0011
Subject:
Mathematics, Probability / Statistics

Particle learning provides a simulation‐based approach to sequential Bayesian computation. To sample from a posterior distribution of interest we use an essential state vector together with a ... More


Modelling Nonlinear Economic Time Series

Timo Teräsvirta, Dag Tjøstheim, and Clive W. J. Granger

Published in print:
2010
Published Online:
May 2011
ISBN:
9780199587148
eISBN:
9780191595387
Item type:
book
Publisher:
Oxford University Press
DOI:
10.1093/acprof:oso/9780199587148.001.0001
Subject:
Economics and Finance, Econometrics

This book contains a up-to-date overview of nonlinear time series models and their application to modelling economic relationships. It considers nonlinear models in stationary and nonstationary ... More


11 Nonlinear and nonstationary models

Timo Teräsvirta, Dag Tjøstheim, and W. J. Granger

in Modelling Nonlinear Economic Time Series

Published in print:
2010
Published Online:
May 2011
ISBN:
9780199587148
eISBN:
9780191595387
Item type:
chapter
Publisher:
Oxford University Press
DOI:
10.1093/acprof:oso/9780199587148.003.0011
Subject:
Economics and Finance, Econometrics

Long memory, unit root models and cointegration are important in linear modelling of nonstationary processes, not the least in econometrics. Recently, nonlinear generalizations of these concepts have ... More


13 Basic nonparametric estimates

Timo Teräsvirta, Dag Tjøstheim, and W. J. Granger

in Modelling Nonlinear Economic Time Series

Published in print:
2010
Published Online:
May 2011
ISBN:
9780199587148
eISBN:
9780191595387
Item type:
chapter
Publisher:
Oxford University Press
DOI:
10.1093/acprof:oso/9780199587148.003.0013
Subject:
Economics and Finance, Econometrics

There are several books on the topics treated in this chapter. For completeness and ease of reference, in the present chapter a brief summary of some results in this area is presented. Among other ... More


16 Building nonlinear models

Timo Teräsvirta, Dag Tjøstheim, and W. J. Granger

in Modelling Nonlinear Economic Time Series

Published in print:
2010
Published Online:
May 2011
ISBN:
9780199587148
eISBN:
9780191595387
Item type:
chapter
Publisher:
Oxford University Press
DOI:
10.1093/acprof:oso/9780199587148.003.0016
Subject:
Economics and Finance, Econometrics

The topic of this chapter is nonlinear model building. Building non‐parametric models is considered first, followed by building various types of parametric nonlinear models. The latter include smooth ... More


Interlude

M. D. Edge

in Statistical Thinking from Scratch: A Primer for Scientists

Published in print:
2019
Published Online:
October 2019
ISBN:
9780198827627
eISBN:
9780191866463
Item type:
chapter
Publisher:
Oxford University Press
DOI:
10.1093/oso/9780198827627.003.0007
Subject:
Biology, Biomathematics / Statistics and Data Analysis / Complexity Studies

This chapter marks a turning point. The preceding two chapters considered probability theory, which describes the kinds of data that result from specified processes. The remainder of the book ... More


A Primer on Nonparametric Methods and Their Application to Research in Human Capital and Economic Growth

in Human Capital and Economic Growth

Published in print:
2008
Published Online:
June 2013
ISBN:
9780804755405
eISBN:
9780804769761
Item type:
chapter
Publisher:
Stanford University Press
DOI:
10.11126/stanford/9780804755405.003.0008
Subject:
Economics and Finance, Econometrics

This chapter outlines basic nonparametric techniques, looking at their specific applications in testing the human capital–growth relationship. The second section provides an overview of nonparametric ... More


Graph Kernels by Spectral Transforms

Zhu Xiaojin, Kandola Jaz, Lafferty John, and Ghahramani Zoubin

in Semi-Supervised Learning

Published in print:
2006
Published Online:
August 2013
ISBN:
9780262033589
eISBN:
9780262255899
Item type:
chapter
Publisher:
The MIT Press
DOI:
10.7551/mitpress/9780262033589.003.0015
Subject:
Computer Science, Machine Learning

This chapter develops an approach to searching over a nonparametric family of spectral transforms by using convex optimization to maximize kernel alignment to the labeled data. Order constraints are ... More


The Lifetime Risk of Nursing Home Use

Michael D. Hurd, Pierre-Carl Michaud, and Susann Rohwedder

in Discoveries in the Economics of Aging

Published in print:
2014
Published Online:
January 2015
ISBN:
9780226146096
eISBN:
9780226146126
Item type:
chapter
Publisher:
University of Chicago Press
DOI:
10.7208/chicago/9780226146126.003.0003
Subject:
Economics and Finance, Public and Welfare

This paper estimates the lifetime risk and distribution of stays in nursing homes using 10 waves of data from the Health and Retirement Study covering the population over the age of 50. Using both ... More


Geometric weight priors and their applications

Ramsés H. Mena

in Bayesian Theory and Applications

Published in print:
2013
Published Online:
May 2013
ISBN:
9780199695607
eISBN:
9780191744167
Item type:
chapter
Publisher:
Oxford University Press
DOI:
10.1093/acprof:oso/9780199695607.003.0014
Subject:
Mathematics, Probability / Statistics

This chapter discusses random probability measures (r.p.m.s) that result in robust choice of nonparametric priors due to their simpler weight structure. The key idea is that having simpler weights ... More


Revisiting Bayesian curve fitting using multivariate normal mixtures ∗

Stephen G Walker and George Karabatsos

in Bayesian Theory and Applications

Published in print:
2013
Published Online:
May 2013
ISBN:
9780199695607
eISBN:
9780191744167
Item type:
chapter
Publisher:
Oxford University Press
DOI:
10.1093/acprof:oso/9780199695607.003.0015
Subject:
Mathematics, Probability / Statistics

This chapter develops a Bayesian nonparametric regression model which relies on a standard Bayesian nonparametric form for the joint distribution of both the dependent and independent variables. The ... More


Bayesian regression structure discovery

Hugh A. Chipman, Edward I George, and Robert E. McCulloch

in Bayesian Theory and Applications

Published in print:
2013
Published Online:
May 2013
ISBN:
9780199695607
eISBN:
9780191744167
Item type:
chapter
Publisher:
Oxford University Press
DOI:
10.1093/acprof:oso/9780199695607.003.0022
Subject:
Mathematics, Probability / Statistics

This chapter describes two different Bayesian approaches that illustrate the vast potential of Bayesian methods to extract information hidden in high-dimensional data. The first is based on the ... More


Surviving fully Bayesian nonparametric regression models

Timothy E. Hanson and Alejandro Jara

in Bayesian Theory and Applications

Published in print:
2013
Published Online:
May 2013
ISBN:
9780199695607
eISBN:
9780191744167
Item type:
chapter
Publisher:
Oxford University Press
DOI:
10.1093/acprof:oso/9780199695607.003.0030
Subject:
Mathematics, Probability / Statistics

This chapter compares two Bayesian nonparametric models that generalize the accelerated failure time model, based on recent work on probability models for predictor-dependent probability ... More


Flexible Bayesian modelling for clustered categorical responses in developmental toxicology

Kottas Athanasios and Fronczyk Kassandra

in Bayesian Theory and Applications

Published in print:
2013
Published Online:
May 2013
ISBN:
9780199695607
eISBN:
9780191744167
Item type:
chapter
Publisher:
Oxford University Press
DOI:
10.1093/acprof:oso/9780199695607.003.0005
Subject:
Mathematics, Probability / Statistics

Developmental toxicity studies investigate birth defects caused by toxic chemicals. This chapter develops a Bayesian nonparametric modelling approach for risk assessment in developmental toxicity ... More


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