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Mathematics and Statistics42%

Selected Abstracts

Local Linear M-estimation in non-parametric spatial regression

JOURNAL OF TIME SERIES ANALYSIS, Issue 3 2009
Zhengyan Lin
primary 62G07; secondary 60F05 Abstract., A robust version of local linear regression smoothers augmented with variable bandwidths is investigated for dependent spatial processes. The (uniform) weak consistency as well as asymptotic normality for the local linear M-estimator (LLME) of the spatial regression function g(x) are established under some mild conditions. Furthermore, an additive model is considered to avoid the curse of dimensionality for spatial processes and an estimation procedure based on combining the marginal integration technique with LLME is applied in this paper. Meanwhile, we present a simulated study to illustrate the proposed estimation method. Our simulation results show that the estimation method works well numerically. [source]

Teaching & Learning Guide for: Moral Realism and Moral Nonnaturalism

PHILOSOPHY COMPASS (ELECTRONIC), Issue 3 2008
Stephen Finlay
Authors' Introduction Metaethics is a perennially popular subject, but one that can be challenging to study and teach. As it consists in an array of questions about ethics, it is really a mix of (at least) applied metaphysics, epistemology, philosophy of language, and mind. The seminal texts therefore arise out of, and often assume competence with, a variety of different literatures. It can be taught thematically, but this sample syllabus offers a dialectical approach, focused on metaphysical debate over moral realism, which spans the century of debate launched and framed by G. E. Moore's Principia Ethica. The territory and literature are, however, vast. So, this syllabus is highly selective. A thorough metaethics course might also include more topical examination of moral supervenience, moral motivation, moral epistemology, and the rational authority of morality. Authors Recommend: Alexander Miller, An Introduction to Contemporary Metaethics (Cambridge: Polity Press, 2003). This is one of the few clear, accessible, and comprehensive surveys of the subject, written by someone sympathetic with moral naturalism. David Brink, Moral Realism and the Foundations of Ethics (Cambridge: Cambridge University Press, 1989). Brink rehabilitates naturalism about moral facts by employing a causal semantics and natural kinds model of moral thought and discourse. Michael Smith, The Moral Problem (Oxford: Blackwell, 1994). Smith's book frames the debate as driven by a tension between the objectivity of morality and its practical role, offering a solution in terms of a response-dependent account of practical rationality. Gilbert Harman and Judith Jarvis Thomson, Moral Relativism & Moral Objectivity (Cambridge, MA: Blackwell, 1996). Harman argues against the objectivity of moral value, while Thomson defends it. Each then responds to the other. Frank Jackson, From Metaphysics to Ethics (Oxford: Clarendon Press, 1998). Jackson argues that reductive conceptual analysis is possible in ethics, offering a unique naturalistic account of moral properties and facts. Mark Timmons, Morality without Foundations (Oxford: Oxford University Press, 1999). Timmons distinguishes moral cognitivism from moral realism, interpreting moral judgments as beliefs that have cognitive content but do not describe moral reality. He also provides a particularly illuminating discussion of nonanalytic naturalism. Philippa Foot, Natural Goodness (New York, NY: Oxford University Press, 2001). A Neo-Aristotelian perspective: moral facts are natural facts about the proper functioning of human beings. Russ Shafer-Landau, Moral Realism: A Defence (New York, NY: Oxford University Press, 2003). In this recent defense of a Moorean, nonnaturalist position, Shafer-Landau engages rival positions in a remarkably thorough manner. Terence Cuneo, The Normative Web (New York, NY: Oxford University Press, 2007). Cuneo argues for a robust version of moral realism, developing a parity argument based on the similarities between epistemic and moral facts. Mark Schroeder, Slaves of the Passions (New York, NY: Oxford University Press, 2007). Schroeder defends a reductive form of naturalism in the tradition of Hume, identifying moral and normative facts with natural facts about agents' desires. Online Materials: PEA Soup: http://peasoup.typepad.com A blog devoted to philosophy, ethics, and academia. Its contributors include many active and prominent metaethicists, who regularly post about the moral realism and naturalism debates. Metaethics Bibliography: http://www.lenmanethicsbibliography.group.shef.ac.uk/Bib.htm Maintained by James Lenman, professor of philosophy at the University of Sheffield, this online resource provides a selective list of published research in metaethics. Stanford Encyclopedia of Philosophy: http://plato.stanford.edu See especially the entries under ,metaethics'. Sample Syllabus: Topics for Lecture & Discussion Note: unless indicated otherwise, all the readings are found in R. Shafer-Landau and T. Cuneo, eds., Foundations of Ethics: An Anthology (Malden: Blackwell, 2007). (FE) Week 1: Realism I (Classic Nonnaturalism) G. E. Moore, Principia Ethica, 2nd ed. (FE ch. 35). W. K. Frankena, ,The Naturalistic Fallacy,'Mind 48 (1939): 464,77. S. Finlay, ,Four Faces of Moral Realism', Philosophy Compass 2/6 (2007): 820,49 [DOI: 10.1111/j.1747-9991.2007.00100.x]. Week 2: Antirealism I (Classic Expressivism) A. J. Ayer, ,Critique of Ethics and Theology' (1952) (FE ch. 3). C. Stevenson, ,The Nature of Ethical Disagreement' (1963) (FE ch. 28). Week 3: Antirealism II (Error Theory) J. L. Mackie, ,The Subjectivity of Values' (1977) (FE ch. 1). R. Joyce, Excerpt from The Myth of Morality (2001) (FE ch. 2). Week 4: Realism II (Nonanalytic Naturalism) R. Boyd, ,How to be a Moral Realist' (1988) (FE ch. 13). P. Railton, ,Moral Realism' (1986) (FE ch. 14). T. Horgan and M. Timmons, ,New Wave Moral Realism Meets Moral Twin Earth' (1991) (FE ch. 38). Week 5: Antirealism III (Contemporary Expressivism) A. Gibbard, ,The Reasons of a Living Being' (2002) (FE ch. 6). S. Blackburn, ,How To Be an Ethical Anti-Realist' (1993) (FE ch. 4). T. Horgan and M. Timmons, ,Nondescriptivist Cognitivism' (2000) (FE ch. 5). W. Sinnott-Armstrong, ,Expressivism and Embedding' (2000) (FE ch. 37). Week 6: Realism III (Sensibility Theory) J. McDowell, ,Values and Secondary Qualities' (1985) (FE ch. 11). D. Wiggins, ,A Sensible Subjectivism' (1991) (FE ch. 12). Week 7: Realism IV (Subjectivism) & Antirealism IV (Constructivism) R. Firth, ,Ethical Absolutism and the Ideal Observer' (1952) (FE ch. 9). G. Harman, ,Moral Relativism Defended' (1975) (FE ch. 7). C. Korsgaard, ,The Authority of Reflection' (1996) (FE ch. 8). Week 8: Realism V (Contemporary Nonnaturalism) R. Shafer-Landau, ,Ethics as Philosophy' (2006) (FE ch. 16). T. M. Scanlon, What We Owe to Each Other (Cambridge, MA: Harvard University Press, 1998), ch. 1. T, Cuneo, ,Recent Faces of Moral Nonnaturalism', Philosophy Compass 2/6 (2007): 850,79 [DOI: 10.1111/j.1747-9991.2007.00102.x]. [source]

Flexible and Robust Implementations of Multivariate Adaptive Regression Splines Within a Wastewater Treatment Stochastic Dynamic Program

QUALITY AND RELIABILITY ENGINEERING INTERNATIONAL, Issue 7 2005
Julia C. C. Tsai
Abstract This paper presents an automatic and more robust implementation of multivariate adaptive regression splines (MARS) within the orthogonal array (OA)/MARS continuous-state stochastic dynamic programming (SDP) method. MARS is used to estimate the future value functions in each SDP level. The default stopping rule of MARS employs the maximum number of basis functions Mmax, specified by the user. To reduce the computational effort and improve the MARS fit for the wastewater treatment SDP model, two automatic stopping rules, which automatically determine an appropriate value for Mmax, and a robust version of MARS that prefers lower-order terms over higher-order terms are developed. Computational results demonstrate the success of these approaches. Copyright © 2005 John Wiley & Sons, Ltd. [source]

Interpreting Statistical Evidence with Empirical Likelihood Functions

BIOMETRICAL JOURNAL, Issue 4 2009
Zhiwei Zhang
Abstract There has been growing interest in the likelihood paradigm of statistics, where statistical evidence is represented by the likelihood function and its strength is measured by likelihood ratios. The available literature in this area has so far focused on parametric likelihood functions, though in some cases a parametric likelihood can be robustified. This focused discussion on parametric models, while insightful and productive, may have left the impression that the likelihood paradigm is best suited to parametric situations. This article discusses the use of empirical likelihood functions, a well-developed methodology in the frequentist paradigm, to interpret statistical evidence in nonparametric and semiparametric situations. A comparative review of literature shows that, while an empirical likelihood is not a true probability density, it has the essential properties, namely consistency and local asymptotic normality that unify and justify the various parametric likelihood methods for evidential analysis. Real examples are presented to illustrate and compare the empirical likelihood method and the parametric likelihood methods. These methods are also compared in terms of asymptotic efficiency by combining relevant results from different areas. It is seen that a parametric likelihood based on a correctly specified model is generally more efficient than an empirical likelihood for the same parameter. However, when the working model fails, a parametric likelihood either breaks down or, if a robust version exists, becomes less efficient than the corresponding empirical likelihood. [source]

Origins and characteristics of Nearctic landbirds in Britain and Ireland in autumn: a statistical analysis

IBIS, Issue 4 2006
IAN A. MCLAREN
We used data from eastern North America in regressions to explain autumn frequencies of Nearctic landbird species in Britain and Ireland (UK-IR). The data were: day-counts of 16 August,15 November from Nova Scotia (NS) on Sable Island 1963,2000 and Seal Island (1963,2002), combined in half-monthly intervals to account for seasonality; published seasonal totals (10- to 11-day intervals, 20 August,10 November 1955,80) of birds killed at a Florida (FL) TV tower; and published counts following a ,Fallout', 11 October 1998, of unseasonal species and southern vagrants in NS, believed to have originated as migrants in the southeast USA that followed a cold front offshore into strong southwest flow beyond. We also used the following species variables: body mass and wing length for size; sd of mass as a proxy for lipid capacity; a five-level index of migratory span (1 for within North America to 5 for almost totally to South America); latitude of easternmost breeding, and distance to nearest normal range to indicate status in NS; a two-level index for day vs. night migrants; an index, where pertinent, of significant population change (0 and 2 for a decrease and increase, respectively, 1 for no change). We also used classification and regression trees to cluster the potential transatlantic vagrants into homogeneous groups based on the explanatory variables. Standard generalized linear model regressions using counts from NS islands and FL produced highly positively skewed residuals (many species too common in UK-IR), but robust regressions eliminated statistical problems, and strengthened effects of non-count variables. Results using Fallout records, representing a subset of longer-distance night migrants, were statistically acceptable. The Fallout list, when supplied with counts from the same species from the NS islands and FL, produced highly significant (R2 = 0.79,0.93) and statistically acceptable regressions that were not improved by robust versions. Overall, the results indicate that October counts, especially of generally larger, longer-distance migrants, best represented those reaching UK-IR. The effect of geographical remoteness was negative , vagrants in NS were less likely to appear in UK-IR. Population changes were important in predicting the 1956,2003 UK-IR counts from 1955,80 FL counts. The seasonal characteristics, high explanatory power of the Fallout list and over-representation of probable over-ocean migrants in the standard regressions all support suggestions by others that many Nearctic vagrants in UK-IR originate in flights off southeast USA and are displaced downwind across the North Atlantic. [source]

Duncan's model for X, -control charts: sensitivity analysis to input parameters

QUALITY AND RELIABILITY ENGINEERING INTERNATIONAL, Issue 1 2010
Cinzia Mortarino
Abstract Duncan's model is a well-known procedure to build a control chart with specific reference to the production process it has to be applied to. Although many papers report true applications proving the procedure's noteworthy economic advantages over control charts set purely on the basis of standard statistical criteria, this method is often perceived only as an academic exercise. Perhaps the greater barrier preventing its practical application stems from the difficulty in making cost items explicit. In this paper a sensitivity analysis is proposed for misspecification in the cost parameters for optimal solutions of Duncan's model. While similar contributions published in the literature perform sensitivity analyses with a one-factor-at-a-time scheme, the original contribution of this paper is represented by the focus given on interactions among changes in values of different cost parameters. The results obtained here denote that all factors significantly affect optimal solutions through quite complicated interactions. This should not, in our opinion, discourage the implementation of Duncan's model, pointing conversely to its robust versions, already available in the current literature. Copyright © 2009 John Wiley & Sons, Ltd. [source]

Testing for Spatial Correlation in Nonstationary Binary Data, with Application to Aberrant Crypt Foci in Colon Carcinogenesis

BIOMETRICS, Issue 4 2003
Tatiyana V. Apanasovich
Summary. In an experiment to understand colon carcinogenesis, all animals were exposed to a carcinogen, with half the animals also being exposed to radiation. Spatially, we measured the existence of what are referred to as aberrant crypt foci (ACF), namely, morphologically changed colonic crypts that are known to be precursors of colon cancer development. The biological question of interest is whether the locations of these ACFs are spatially correlated: if so, this indicates that damage to the colon due to carcinogens and radiation is localized. Statistically, the data take the form of binary outcomes (corresponding to the existence of an ACF) on a regular grid. We develop score-type methods based upon the Matern and conditionally autoregressive (CAR) correlation models to test for the spatial correlation in such data, while allowing for nonstationarity. Because of a technical peculiarity of the score-type test, we also develop robust versions of the method. The methods are compared to a generalization of Moran's test for continuous outcomes, and are shown via simulation to have the potential for increased power. When applied to our data, the methods indicate the existence of spatial correlation, and hence indicate localization of damage. [source]