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Iterative Proportional Fitting
The iterative proportional fitting procedure (IPF or IPFP, also known as biproportional fitting or biproportion in statistics or economics (input-output analysis, etc.), RAS algorithm in economics, raking in survey statistics, and matrix scaling in computer science) is the operation of finding the fitted matrix X which is the closest to an initial matrix Z but with the row and column totals of a target matrix Y (which provides the constraints of the problem; the interior of Y is unknown). The fitted matrix being of the form X=PZQ, where P and Q are diagonal matrices such that X has the margins (row and column sums) of Y. Some algorithms can be chosen to perform biproportion. We have also the entropy maximization, information loss minimization (or cross-entropy) or RAS which consists of factoring the matrix rows to match the specified row totals, then factoring its columns to match the specified column totals; each step usually disturbs the previous step's match, so these steps are ...
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SIAM Journal On Matrix Analysis And Applications
The ''SIAM Journal on Matrix Analysis and Applications'' is a peer-reviewed scientific journal covering matrix analysis and its applications. The relevant applications include signal processing, systems and control theory, statistics, Markov chains, mathematical biology, graph theory, and data science. The journal was originally established as the ''SIAM Journal on Algebraic and Discrete Methods'' in 1980, until it split into '' SIAM Journal on Discrete Mathematics'' and the current title in 1988. The journal is published by the Society for Industrial and Applied Mathematics. The founding editor-in-chief An editor-in-chief (EIC), also known as lead editor or chief editor, is a publication's editorial leader who has final responsibility for its operations and policies. The editor-in-chief heads all departments of the organization and is held accoun ... was Gene H. Golub, who established the journal in 1980. The current editor is Michele Benzi ( Scuola Normale Superiore). Re ...
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Biproportional Apportionment
Biproportional apportionment is a proportional representation method to allocate seats in proportion to two separate characteristics. That is, for two different partitions each part receives the proportional number of seats within the total number of seats. For instance, this method could give proportional results by party and by region, or by party and by gender/ethnicity, or by any other pair of characteristics. # Example: proportional by party and by region #* Each party's share of seats is proportional to its total votes. #* Each region's share of seats is proportional to its total votes #** (or this could be based on its population-size or other criteria). # Then, as nearly as possible given the totals for each region and each party: #* Each region's seats are allocated among parties in proportion to that region's votes for those parties. (The region's seats go to locally popular parties.) #* Each party's seats are allocated among regions in proportion to that party's votes i ...
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Triangulation (social Science)
In the social sciences, triangulation refers to the application and combination of several research methods in the study of the same phenomenon. By combining multiple observers, theories, methods, and empirical materials, researchers hope to overcome the weakness or intrinsic biases and the problems that come from single method, single-observer, and single-theory studies. It is popularly used in sociology. "The concept of triangulation is borrowed from navigational and land surveying techniques that determine a single point in space with the convergence of measurements taken from two other distinct points." Triangulation can be used in both quantitative and qualitative studies as an alternative to traditional criteria like reliability and validity. Purpose The purpose of triangulation in qualitative research is to increase the credibility and validity of the results. Several scholars have aimed to define triangulation throughout the years. *Cohen and Manion (2000) define tria ...
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Data Editing
Data editing is defined as the process involving the review and adjustment of collected survey data. Data editing helps define guidelines that will reduce potential bias and ensure consistent estimates leading to a clear analysis of the data set by correct inconsistent data using the methods later in this article. The purpose is to control the quality of the collected data. Data editing can be performed manually, with the assistance of a computer or a combination of both. Editing methods Editing methods refer to a range of procedures and processes which are used for detecting and handling errors in data. Data editing is used with the goal to improve the quality of statistical data produced. These modifications can greatly improve the quality of analytics created by aiming to detect and correct errors. Examples of different techniques to data editing such as micro-editing, macro-editing, selective editing, or the different tools used to achieve data editing such as graphical editing a ...
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Data Cleansing
Data cleansing or data cleaning is the process of identifying and correcting (or removing) corrupt, inaccurate, or irrelevant records from a dataset, table, or database. It involves detecting incomplete, incorrect, or inaccurate parts of the data and then replacing, modifying, or deleting the affected data. Data cleansing can be performed interactively using data wrangling tools, or through batch processing often via scripts or a data quality firewall. After cleansing, a data set should be consistent with other similar data sets in the system. The inconsistencies detected or removed may have been originally caused by user entry errors, by corruption in transmission or storage, or by different data dictionary definitions of similar entities in different stores. Data cleaning differs from data validation in that validation almost invariably means data is rejected from the system at entry and is performed at the time of entry, rather than on batches of data. The actual process ...
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Open Science Framework
The Center for Open Science is a non-profit technology organization based in Charlottesville, Virginia with a mission to "increase the openness, integrity, and reproducibility of scientific research." Brian Nosek and Jeffrey Spies founded the organization in January 2013, funded mainly by the Laura and John Arnold Foundation and others. The organization began with work in reproducibility of psychology research, with the large-scale initiative Reproducibility Project: Psychology. A second reproducibility project for cancer biology research has also been started through a partnership with Science Exchange (company), Science Exchange. In March 2017, the Center published a detailed strategic plan. Brian Nosek posted a letter outlining the history of the Center and future directions. In 2020, the Center received a grant from Fast Grants to promote the publication of COVID-19 research on the platform. In 2021, the Center for Open Science was honored with the in the institutional cat ...
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Maximum Likelihood Estimation
In statistics, maximum likelihood estimation (MLE) is a method of estimation theory, estimating the Statistical parameter, parameters of an assumed probability distribution, given some observed data. This is achieved by Mathematical optimization, maximizing a likelihood function so that, under the assumed statistical model, the Realization (probability), observed data is most probable. The point estimate, point in the parameter space that maximizes the likelihood function is called the maximum likelihood estimate. The logic of maximum likelihood is both intuitive and flexible, and as such the method has become a dominant means of statistical inference. If the likelihood function is Differentiable function, differentiable, the derivative test for finding maxima can be applied. In some cases, the first-order conditions of the likelihood function can be solved analytically; for instance, the ordinary least squares estimator for a linear regression model maximizes the likelihood when ...
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Journal Of Demographic Economics
A journal, from the Old French ''journal'' (meaning "daily"), may refer to: *Bullet journal, a method of personal organization *Diary, a record of personal secretive thoughts and as open book to personal therapy or used to feel connected to oneself. A record of what happened over the course of a day or other period *Daybook, also known as a general journal, a daily record of financial transactions *Logbook, a record of events important to the operation of a vehicle, facility, or otherwise * Transaction log, a chronological record of data processing * Travel journal, a record of the traveller's experience during the course of their journey In publishing, ''journal'' can refer to various periodicals or serials: *Academic journal, an academic or scholarly periodical ** Scientific journal, an academic journal focusing on science ** Medical journal, an academic journal focusing on medicine ** Law review, a professional journal focusing on legal interpretation *Magazine, non-academic ...
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NM-method
The NM-method or Naszodi–Mendonca method is the operation that can be applied in statistics, econometrics, economics, sociology, and demography to construct counterfactual contingency tables. The method finds the matrix X ( X \in \mathbb^ ) which is "closest" to matrix Z ( Z \in \mathbb^ called the seed table) in the sense of being #Definition of matrix ranking, ranked the same but with the #Constraints on the row totals and column totals, row and column totals of a target matrix Y ( Y \in \mathbb^) . While the row totals and column totals of Y are known, matrix Y itself may not be known. Since the #Solution, solution for matrix X is unique, the NM-method is a function: X=\text(Z, Y e^T_m, e_nY): \mathbb^ \times \mathbb^ \times \mathbb^ \mapsto \mathbb^, where e_n is a row vector of ones of size 1\times n, while e^T_m is a column vector of ones of size m\times 1. The NM-method was developed by Naszodi and Mendonca (2021) (and first applied by Naszodi and Mendonca (2019) to sol ...
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Preconditioner
In mathematics, preconditioning is the application of a transformation, called the preconditioner, that conditions a given problem into a form that is more suitable for numerical solving methods. Preconditioning is typically related to reducing a condition number of the problem. The preconditioned problem is then usually solved by an iterative method. Preconditioning for linear systems In linear algebra and numerical analysis, a preconditioner P of a matrix A is a matrix such that P^A has a smaller condition number than A. It is also common to call T=P^ the preconditioner, rather than P, since P itself is rarely explicitly available. In modern preconditioning, the application of T = P^, i.e., multiplication of a column vector, or a block of column vectors, by T = P^, is commonly performed in a matrix-free fashion, i.e., where neither P, nor T = P^ (and often not even A) are explicitly available in a matrix form. Preconditioners are useful in iterative methods to solve ...
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Contingency Tables
In statistics, a contingency table (also known as a cross tabulation or crosstab) is a type of table in a matrix format that displays the multivariate frequency distribution of the variables. They are heavily used in survey research, business intelligence, engineering, and scientific research. They provide a basic picture of the interrelation between two variables and can help find interactions between them. The term ''contingency table'' was first used by Karl Pearson in "On the Theory of Contingency and Its Relation to Association and Normal Correlation", part of the '' Drapers' Company Research Memoirs Biometric Series I'' published in 1904. A crucial problem of multivariate statistics is finding the (direct-)dependence structure underlying the variables contained in high-dimensional contingency tables. If some of the conditional independences are revealed, then even the storage of the data can be done in a smarter way (see Lauritzen (2002)). In order to do this one can use in ...
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Frederick F
Frederick may refer to: People * Frederick (given name), the name Given name Nobility = Anhalt-Harzgerode = *Frederick, Prince of Anhalt-Harzgerode (1613–1670) = Austria = * Frederick I, Duke of Austria (Babenberg), Duke of Austria from 1195 to 1198 * Frederick II, Duke of Austria (1219–1246), last Duke of Austria from the Babenberg dynasty * Frederick the Fair (Frederick I of Austria (Habsburg), 1286–1330), Duke of Austria and King of the Romans = Baden = * Frederick I, Grand Duke of Baden (1826–1907), Grand Duke of Baden * Frederick II, Grand Duke of Baden (1857–1928), Grand Duke of Baden = Bohemia = * Frederick, Duke of Bohemia (died 1189), Duke of Olomouc and Bohemia = Britain = * Frederick, Prince of Wales (1707–1751), eldest son of King George II of Great Britain = Brandenburg/Prussia = * Frederick I, Elector of Brandenburg (1371–1440), also known as Frederick VI, Burgrave of Nuremberg * Frederick II, Elector of Brandenburg (1413–1470), Margrave of ...
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