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RAS Algorithm
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 ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
SIAM Journal On Matrix Analysis And Applications
The ''SIAM Journal on Matrix Analysis and Applications'' (until 1989: ''SIAM Journal on Algebraic and Discrete Methods'') 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 is published by the Society for Industrial and Applied Mathematics. The founding editor-in-chief was Gene H. Golub, who established the journal in 1980. The current editor is Michele Benzi (Scuola Normale Superiore). See also *Michele Benzi Michele Benzi (born 1962 in Bologna) is an Italian mathematician who works as a full professor in the Scuola Normale Superiore in Pisa. He is known for his contributions to numerical linear algebra and its applications, especially to the solu ... External links * Mathematics journals Publications established in 1980 English-language journals Quarterly jou ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
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 ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
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 trian ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
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 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 editings such as graphical editing and inter ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Data Cleansing
Data cleansing or data cleaning is the process of detecting and correcting (or removing) corrupt or inaccurate records from a record set, table, or database and refers to identifying incomplete, incorrect, inaccurate or irrelevant parts of the data and then replacing, modifying, or deleting the dirty or coarse data. Data cleansing may be performed interactively with data wrangling tools, or as batch processing through scripting 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 of ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Maximum Likelihood Estimation
In statistics, maximum likelihood estimation (MLE) is a method of estimating the parameters of an assumed probability distribution, given some observed data. This is achieved by maximizing a likelihood function so that, under the assumed statistical model, the observed data is most probable. The 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, 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 all observed outcomes are assumed to have Normal distributions with the same variance. From the perspective of Bayesian inference, M ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Journal Of Demographic Economics
''Journal of Demographic Economics'' (JODE) is a peer-reviewed academic journal at the intersection of demography and economics. It is published by Cambridge University Press and edited by the Institute of Economic and Social Research of the UCLouvain. The Journal of Demographic Economics publishes four issues a year. The Journal of the Demographic Economics (JODE) welcomes both empirical and theoretical papers on issues relevant to Demographic Economics with a preference for combining abstract economic or demographic models together with data to highlight major mechanisms of the interplay between demographics and economics. JODE intends to be the premier demography & economics outlet for empirical contributions that are firmly grounded in theory as well as theoretical papers that are motivated by empirical regularities and findings. The editor-in-chief of JODE is David de la Croix (UClouvain) and Murat Iyigun (University of Colorado at Boulder) is the Co-Editor. In August 2021, ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
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 ranked the same but with the 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 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 an all one row vector of size 1\times n, while e^T_m is an all one column vector of size m\times 1. The NM-method was developed by Naszodi and Mendonca (2021) to solve for matrix X in problems, where matrix \boldsymbol is not a sample from the population characterized by the row totals and ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
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 a line ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
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 ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Frederick F
Frederick may refer to: People * Frederick (given name), the 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 Brandenburg * Frederick William, Elector ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Input–output Model
In economics, an input–output model is a quantitative economic model that represents the interdependencies between different sectors of a national economy or different regional economies.Thijs Ten Raa, Input–Output Economics: Theory and Applications: Featuring Asian Economies', World Scientific, 2009 Wassily Leontief (1906–1999) is credited with developing this type of analysis and earned the Nobel Prize in Economics for his development of this model. Origins Francois Quesnay had developed a cruder version of this technique called Tableau économique, and Léon Walras's work ''Elements of Pure Economics'' on general equilibrium theory also was a forerunner and made a generalization of Leontief's seminal concept. Alexander Bogdanov has been credited with originating the concept in a report delivered to the All Russia Conference on the Scientific Organisation of Labour and Production Processes, in January 1921. This approach was also developed by L. N. Kritsman and T. F. ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
