9,469 research outputs found
Functional Structure and Approximation in Econometrics (book front matter)
This is the front matter from the book, William A. Barnett and Jane Binner (eds.), Functional Structure and Approximation in Econometrics, published in 2004 by Elsevier in its Contributions to Economic Analysis monograph series. The front matter includes the Table of Contents, Volume Introduction, and Section Introductions by Barnett and Binner and the Preface by W. Erwin Diewert. The volume contains a unified collection and discussion of W. A. Barnett's most important published papers on applied and theoretical econometric modelling.consumer demand, production, flexible functional form, functional structure, asymptotics, nonlinearity, systemwide models
Decolonising Mathematics: How and why it makes science better (and enables students to solve harder problems)
Mathematics is not universal. Traditional normal mathematics accepted both empirical proofs and reasoning, as does science, but formal mathematics prohibits the empirical. Prohibiting the empirical is obviously disadvantageous for applications of mathematics to science, but colonial education anyway replaced normal by formal math, declaring the latter to be superior without any critical examination, and globalised it
Fence methods for mixed model selection
Many model search strategies involve trading off model fit with model
complexity in a penalized goodness of fit measure. Asymptotic properties for
these types of procedures in settings like linear regression and ARMA time
series have been studied, but these do not naturally extend to nonstandard
situations such as mixed effects models, where simple definition of the sample
size is not meaningful. This paper introduces a new class of strategies, known
as fence methods, for mixed model selection, which includes linear and
generalized linear mixed models. The idea involves a procedure to isolate a
subgroup of what are known as correct models (of which the optimal model is a
member). This is accomplished by constructing a statistical fence, or barrier,
to carefully eliminate incorrect models. Once the fence is constructed, the
optimal model is selected from among those within the fence according to a
criterion which can be made flexible. In addition, we propose two variations of
the fence. The first is a stepwise procedure to handle situations of many
predictors; the second is an adaptive approach for choosing a tuning constant.
We give sufficient conditions for consistency of fence and its variations, a
desirable property for a good model selection procedure. The methods are
illustrated through simulation studies and real data analysis.Comment: Published in at http://dx.doi.org/10.1214/07-AOS517 the Annals of
Statistics (http://www.imstat.org/aos/) by the Institute of Mathematical
Statistics (http://www.imstat.org
The concept of "character" in Dirichlet's theorem on primes in an arithmetic progression
In 1837, Dirichlet proved that there are infinitely many primes in any
arithmetic progression in which the terms do not all share a common factor. We
survey implicit and explicit uses of Dirichlet characters in presentations of
Dirichlet's proof in the nineteenth and early twentieth centuries, with an eye
towards understanding some of the pragmatic pressures that shaped the evolution
of modern mathematical method
Preface: Challenging the Politics of the Teacher Accountability Movement
Explains that this issue is intended as a resource for anyone concerned with re-framing and taking back the educational conversation, moving toward meaningful school reform that is based in a commitment to creating conditions under which teachers can develop the kinds of complex and sophisticated professional knowledges and practices that support authentic student learning
Infinity
This essay surveys the different types of infinity that occur in pure and applied mathematics, with emphasis on: 1. the contrast between potential infinity and actual infinity; 2. Cantor's distinction between transfinite sets and absolute infinity; 3. the constructivist view of infinite quantifiers and the meaning of constructive proof; 4. the concept of feasibility and the philosophical problems surrounding feasible arithmetic; 5. Zeno's paradoxes and modern paradoxes of physical infinity involving supertasks
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