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The Dual of the Least-Squares Method  [PDF]
Quirino Paris
Open Journal of Statistics (OJS) , 2015, DOI: 10.4236/ojs.2015.57067
Abstract:

This paper presents the dual specification of the least-squares method. In other words, while the traditional (primal) formulation of the method minimizes the sum of squared residuals (noise), the dual specification maximizes a quadratic function that can be interpreted as the value of sample information. The two specifications are equivalent. Before developing the methodology that describes the dual of the least-squares method, the paper gives a historical perspective of its origin that sheds light on the thinking of Gauss, its inventor. The least-squares method is firmly established as a scientific approach by Gauss, Legendre and Laplace within the space of a decade, at the beginning of the nineteenth century. Legendre was the first author to name the approach, in 1805, as “méthode des moindres carrés”, a “least-squares method”. Gauss, however, used the method as early as 1795, when he was 18 years old. Again, he adopted it in 1801 to calculate the orbit of the newly discovered planet Ceres. Gauss published his way of looking at the least-squares approach in 1809 and gave several hints that the least-squares algorithm was a minimum variance linear estimator and that it was derivable from maximum likelihood considerations. Laplace wrote a very substantial chapter about the method in his fundamental treatise on probability theory published in 1812.


The Dual of the Maximum Likelihood  [PDF]
Quirino Paris
Open Journal of Statistics (OJS) , 2016, DOI: 10.4236/ojs.2016.61016
Abstract: The Maximum Likelihood method estimates the parameter values of a statistical model that maximizes the corresponding likelihood function, given the sample information. This is the primal approach that, in this paper, is presented as a mathematical programming specification whose solution requires the formulation of a Lagrange problem. A result of this setup is that the Lagrange multipliers associated with the linear statistical model (where sample observations are regarded as a set of constraints) are equal to the vector of residuals scaled by the variance of those residuals. The novel contribution of this paper consists in deriving the dual model of the Maximum Likelihood method under normality assumptions. This model minimizes a function of the variance of the error terms subject to orthogonality conditions between the model residuals and the space of explanatory variables. An intuitive interpretation of the dual problem appeals to basic elements of information theory and an economic interpretation of Lagrange multipliers to establish that the dual maximizes the net value of the sample information. This paper presents the dual ML model for a single regression and provides a numerical example of how to obtain maximum likelihood estimates of the parameters of a linear statistical model using the dual specification.
Estimation of CARA Preferences and Positive Mathematical Programming  [PDF]
Quirino Paris
Open Journal of Statistics (OJS) , 2018, DOI: 10.4236/ojs.2018.81001
Abstract: The purpose of this paper is to combine the estimation of output price risk and positive mathematical programming (PMP). It reconciles the risk programming presented by Freund with a consistent estimate of the constant absolute risk aversion (CARA) coefficient. It extends the PMP approach to calibration of realized production outputs and observed input prices. The results of this specification include 1) uniqueness of the calibrating solution, 2) elimination of the tautological calibration constraints typical of the original PMP procedure, 3) equivalence between a phase I calibrating solution and a solution obtained by combining phase I and phase II of the traditional PMP procedure. In this extended PMP framework, the cost function specification involves output quantities and input prices—contrary to the myopic cost function of the traditional PMP approach. This extension allows for a phase III calibrating model that replaces the usual linear technology with relations corresponding to Shephard lemma (in the primal constraints) and the marginal cost function (in the dual constraints). An empirical example with a sample of farms producing four crops illustrates the novel procedure.
Testing the Adding up Condition in Demand Systems  [PDF]
Quirino Paris, Francesco Caracciolo
Open Journal of Statistics (OJS) , 2017, DOI: 10.4236/ojs.2017.72022
Abstract: A test of the adding up condition in demand systems is crucial for determining whether a share format is admissible when the number of sample goods is smaller than the number of commodity choices available to consumers. This test requires the estimation of a demand system in a quantity format. It cannot be performed when a demand system is specified in share format. The share specification of any demand system is like a straight jacket: once worn, it forces the error covariance matrix to be singular and the adding up condition to hold whether or not the data generating process warrants it. The empirical verification of the adding up hypothesis uses a five-commodity sample selected from the Canadian Family Expenditure Survey with 4847 observations. Three specifications are considered: AIDS (Almost Ideal Demand System), QUAIDS (Quadratic AIDS) and EASI (Exact Affine Stone Index). The hypothesis is rejected in all three cases with a high level of confidence.
Asking the Right Questions: The Role of the Conservator in Digital Projects
Jan Paris
Liber Quarterly : The Journal of European Research Libraries , 2008,
Abstract: Jan Paris, conservator at the library of the University of North Carolina (Chapel Hill) explains how she decides whether vulnerable material from the special collections may be digitized and under what conditions. She considers not only the condition of the objects, but also the purpose of the digitization process: education, preservation, creating a facsimile edition or as part of a large-scale preservation project. These can be summarized as the impact of preservation considerations such as the reduction in handling, the reduction in the need for interventive conservation and the impact of access considerations such as enabling value-added research, on-demand digitization and producing aids to teaching.
Breaking the Mould: How Re-examining the Allocation Formula Led to the Creation of a Dynamic Role for the University's Librarians
Terrence Paris
Partnership : the Canadian Journal of Library and Information Practice and Research , 2007,
Abstract: A modestly conceived proposal to change a long established allocation formula rapidly evolved into a new model of library service. The new model created five discipline funds groups: Humanities, Social Sciences, Sciences, Educational Studies and Business Studies and the assignment of liaison tasks to the five professional librarians and the archivist. The goal of creating a fairer allocation was superseded by more substantive goals intended to: loosen the ties of collections funding to 24 departments by funding groups of cognate disciplines and unique programs of interdisciplinary instruction and research; involve all librarians in the task of collection analysis and development; redefine librarian positions to promote their contribution as full partners with classroom faculty in solving problems and improving research and teaching. Along with improved collections, the ultimate goal is a full integration of the librarians’ professional expertise with the University's newly drafted strategic plan.
Medici obiettori e consultori pubblici. Nota a T.A.R. Puglia (Bari), sez. II, 14 settembre 2010, n. 3477
Davide Paris
Stato, Chiese e Pluralismo Confessionale , 2011,
Abstract: Il contributo è stato segnalato dal Prof. Roberto Mazzola, dell’Università del Piemonte orientale. SOMMARIO: 1. Introduzione – 2. La ratio decidendi: l’(inaccettabile) interpretazione restrittiva dell’ambito di applicazione dell’obiezione di coscienza – 3. La contraddittorietà della pronuncia – 4. Una vittoria per gli obiettori di coscienza?
Breaking the Mould: How Re-examining the Allocation Formula Led to the Creation of a Dynamic Role for the University's Librarians
Terrence Paris
Partnership : the Canadian Journal of Library and Information Practice and Research , 2007,
Abstract: A modestly conceived proposal to change a long established allocation formula rapidly evolved into a new model of library service. The new model created five discipline fund groups: Humanities, Social Sciences, Sciences, Educational Studies and Business Studies and the assignment of liaison tasks to the five professional librarians and the archivist. The goal of creating a fairer allocation was superseded by more substantive goals intended to: loosen the ties of collections funding to 24 departments by funding groups of cognate disciplines and unique programs of interdisciplinary instruction and research; involve all librarians in the task of collection analysis and development; and redefine librarian positions to promote their contribution as full partners with classroom faculty in solving problems and improving research and teaching. Along with improved collections, the ultimate goal was a full integration of the librarians’ professional expertise with the University's newly drafted strategic plan.
Lille, de la métropole à la région urbaine
Didier Paris
Mappemonde , 2002,
Abstract: Depuis la fin des années 1980, le développement de Lille s'inscrit dans le cadre d'une stratégie de métropolisation. Celle-ci passe notamment par l'aptitude des acteurs politiques et économiques locaux à se mobiliser dans une dynamique de gouvernance et ne peut faire l'impasse sur le grand enjeu d'aménagement et de solidarité que représente la nécessité du renouvellement urbain. Ce processus s'articule à un système régional transfrontalier à forte densité et structuré en réseaux de villes très proches.
Nazismo y populismo: una aproximación historiográfica
Paolo Paris
Identidades , 2012,
Abstract: Este trabajo va a intentar dar respuesta a algunos interrogantes recurrentes sobre el funcionamiento político del nazismo relacionado sobre todo a su carácter populista. A través de un recorrido historiográfico y apoyándome en la teoría de Ernesto Laclau, pretendo explorar la vaguedad e indeterminación del discurso nazi, tanto en cuanto al público al que se dirige como en sus postulados políticos. El recorrido historiográfico incluirá a: Patricio Geli, Eric Hobsbawm y Jorge Saborido. A través de sus propuestas trataré de establecer un estado de la cuestión sobre la historiografía referida al nazismo, su surgimiento, su composición, su ‘ideología’, el papel del líder, el papel de las masas, su funcionamiento político hacia el interior y hacia el exterior de Alemania. Para luego introducir la crítica de Laclau, basada en una noción de sujeto que surge de nuevos aportes de la psicología, la lingüística y la filosofía. Esto nos llevará a revisar las explicaciones sobre el nazismo propuestas hasta el momento y cuestionarla mirada de la historia, revisando varios conceptos transversales comoidentidad, política, democracia, pueblo, clase, objetividad, sociedad, hegemonía, discurso, líder, etc.
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