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- Generalized least-squares regression (2)
- Geometric mean regression (2)
- Least-squares (2)
- Orthogonal regression (2)
- Symmetric least-squares (2)
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- Weighted ordinary least-squares (2)
- Birthday problem. (1)
- Central Limit Theorem (1)
- DEA analytical solutions (1)
- Data Envelopment Analysis (1)
- Efficiency decomposition (1)
- Environmental efficiency (1)
- Monte Carlo simulations (1)
- Programming in R (1)
- Stochastic DEA with a perfect object (1)
- Student projects in probability (1)
Articles 1 - 4 of 4
Full-Text Articles in Physical Sciences and Mathematics
Stochastic Dea With A Perfect Object And Its Application To Analysis Of Environmental Efficiency, Alexander Vaninsky
Stochastic Dea With A Perfect Object And Its Application To Analysis Of Environmental Efficiency, Alexander Vaninsky
Publications and Research
The paper introduces stochastic DEA with a Perfect Object (SDEA PO). The Perfect Object (PO) is a virtual Decision Making Unit (DMU) that has the smallest inputs and greatest outputs. Including the PO in a collection of actual objects yields an explicit formula of the efficiency index. Given the distributions of DEA inputs and outputs, this formula allows us to derive the probability distribution of the efficiency score, to find its mathematical expectation, and to deliver common (group–related) and partial (object-related) efficiency components. We apply this approach to a prospective analysis of environmental efficiency of the major national and regional …
Simulation Insights Using R, Boyan Kostadinov
Simulation Insights Using R, Boyan Kostadinov
Publications and Research
This article attempts to introduce the reader to computational thinking and solving problems involving randomness. The main technique being employed is the Monte Carlo method, using the freely available software R for Statistical Computing. The author illustrates the computer simulation approach by focusing on several problems of increasing difficulty. The simulation techniques and the specific problems discussed in this article would be of interest to STEM students and instructors, teaching courses in Monte Carlo simulations, stochastic modeling, probability and statistics. The R code for all problems is discussed in full detail so that the reader can get a taste of …
Generalized Least-Squares Regressions I: Efficient Derivations, Nataniel Greene
Generalized Least-Squares Regressions I: Efficient Derivations, Nataniel Greene
Publications and Research
Ordinary least-squares regression suffers from a fundamental lack of symmetry: the regression line of y given x and the regression line of x given y are not inverses of each other. Alternative symmetric regression methods have been developed to address this concern, notably: orthogonal regression and geometric mean regression. This paper presents in detail a variety of least squares regression methods which may not have been known or fully explicated. The derivation of each method is made efficient through the use of Ehrenberg's formula for the ordinary least-squares error and through the extraction of a weight function g(b) which characterizes …
Generalized Least-Squares Regressions Ii: Theory And Classification, Nataniel Greene
Generalized Least-Squares Regressions Ii: Theory And Classification, Nataniel Greene
Publications and Research
In the first paper of this series, a variety of known and new symmetric and weighted least-squares regression methods were presented with efficient derivations. This paper continues and generalizes the previous work with a theory for deriving, analyzing, and classifying all symmetric and weighted least-squares regression methods.