scholarly journals On the Geometric Mean Method for Incomplete Pairwise Comparisons

Mathematics ◽  
2020 ◽  
Vol 8 (11) ◽  
pp. 1873
Author(s):  
Konrad Kułakowski
Keyword(s):  
Least Squares ◽  
Least Squares Method ◽  
Geometric Mean ◽  
Computational Method ◽  
Pairwise Comparisons ◽  
Similar Relationship ◽  
Final Solution ◽  
The Difference ◽  
The Relationship ◽  
Theoretical Considerations

One of the most popular methods of calculating priorities based on the pairwise comparisons matrices (PCM) is the geometric mean method (GMM). It is equivalent to the logarithmic least squares method (LLSM), so some use both names interchangeably, treating it as the same approach. The main difference, however, is in the way the calculations are done. It turns out, however, that a similar relationship holds for incomplete matrices. Based on Harker’s method for the incomplete PCM, and using the same substitution for the missing entries, it is possible to construct the geometric mean solution for the incomplete PCM, which is fully compatible with the existing LLSM for the incomplete PCM. Again, both approaches lead to the same results, but the difference is how the final solution is computed. The aim of this work is to present in a concise form, the computational method behind the geometric mean method (GMM) for an incomplete PCM. The computational method is presented to emphasize the relationship between the original GMM and the proposed solution. Hence, everyone who knows the GMM for a complete PCM should easily understand its proposed extension. Theoretical considerations are accompanied by a numerical example, allowing the reader to follow the calculations step by step.

scholarly journals COMPARISON OF CLASSIFICATION ABILITY INDICES OF PARAMETERS CHARACTERIZING THE STEREOMETRIC FEATURES OF TECHNICAL SURFACES

2018 ◽  
Vol 18 (3) ◽  
pp. 99-108
Author(s):  
Rafal ROZANSKI
Keyword(s):  
Least Squares ◽  
Least Squares Method ◽  
Geometric Mean ◽  
Machining Processes ◽  
Two Indices ◽  
Comparison Of The Results ◽  
Parameter Values ◽  
The Relationship

The study examined the relationship between the values of two indices evaluating the classification capacity of parameters characterizing the stereometric features of technical surfaces. The values of 83 3D parameters characterizing the stereometric features for 22 surfaces created in various machining processes were taken into account. The examined surfaces differ significantly in the stereometric characteristics of the surface with the similar value of the St parameter. The variance and the geometric mean of ordered parameter values differences were used as the indices of parameters classification ability. In particular, the existence, type and strength of relationship between the adopted indices were evaluated, and the model of the relationship between the indices was determined using the least-squares method. A comparison of the results obtained with those obtained from the analogous evaluation for 8 types of theoretical distributions of parameter values was also carried out.

scholarly journals Econometric Analysis of Dynamics of Personnel Training in Tourism Sphere

2021 ◽  
Vol 12 (6) ◽  
pp. 1389-1396
Author(s):  
Anar Eminov Et al.
Keyword(s):  
Least Squares ◽  
Statistical Data ◽  
Least Squares Method ◽  
Tourism Industry ◽  
Econometric Analysis ◽  
Steady Increase ◽  
Foreign Nationals ◽  
Tourism Sector ◽  
Analysis Of Dynamics ◽  
The Relationship

According to the statistical data of recent years, tourism has been one of the ever-growing sectors in Azerbaijan. Thus, in the last five years, there has been a steady increase in the number of entrepreneurship subjects serving tourism in Azerbaijan and the number of foreign nationals traveling for tourism, correspondingly 4.5 and 8.5 percent. At present, the direct share of the tourism industry in the country's GDP and employment is 4.5 and 3.3 percent, respectively. In the article econometric analysis of the dependence on the relationship between tourism industry graduates and their development has been done. The regression equation of the dependence of the number of graduates studying tourism on the number of tourists in the country and the dependence of the tourism sector’s GDP on the number of graduates in the tourism sector were estimated using the Eviews software based on 2008–2017 statistical data using the least squares method.

Financial disclosure and performance of microfinance institutions

2014 ◽  
Vol 10 (3) ◽  
pp. 314-337 ◽  
Author(s):  
Shakil Quayes ◽  
Tanweer Hasan
Keyword(s):  
Financial Performance ◽  
Least Squares ◽  
Least Squares Method ◽  
Financial Disclosure ◽  
Microfinance Institutions ◽  
Content Type ◽  
Three Stage Least Squares ◽  
And Performance ◽  
The Impact ◽  
The Relationship

Purpose – The purpose of this paper is to analyze the relationship between financial disclosure and the financial performance of microfinance institutions (MFIs). Design/methodology/approach – The paper utilizes ordinary least squares method to analyze the impact of disclosure on financial performance, an ordered probit model to investigate the possible effect of financial performance on disclosure and utilizes a three-stage least squares method to delineate the endogenous relationship between disclosure and financial performance of MFIs. Findings – The paper finds that better disclosure has a statistically significant positive impact on operational performance of MFIs; second, it also shows that improved financial performance results in better financial disclosure. Keeping the endogenous nature of the relationship between disclosure and performance, the paper uses a three-stage least squares method to show that disclosure and financial performance positively affect each other simultaneously. Research limitations/implications – The paper attempts to delineate a positive association between better disclosure on financial performance of MFIs, which can be used for developing a better disclosure policy by management, formulating more effective guidelines for disclosure by the stakeholders and mandating more appropriate laws and uniform disclosure practice by regulators. Originality/value – This is the first study that uses a large number of MFIs from 75 countries; second, it uses a uniform scale of designating a disclosure rating (assigned by MIX Market) to show the relationship between disclosure and performance. Finally, it uses three-stage least squares method to address the possible endogeneity between disclosure and performance.

scholarly journals About the features of the least squares method with linearization when determining nonlinear parameters of functional dependencies

2021 ◽  
Vol 2131 (2) ◽  
pp. 022132
Author(s):  
Lidia V Azarova
Keyword(s):  
Parameter Estimation ◽  
Least Squares ◽  
Empirical Data ◽  
Least Squares Method ◽  
Functional Dependence ◽  
Functional Dependencies ◽  
Final Solution ◽  
Two Stage ◽  
Theoretical Dependence ◽  
Nonlinear Parameters

Abstract The features of approximation of empirical data by functional dependence with nonlinear parameters using the two-stage least squares method are considered in this paper. A method of simplified parameter estimation by constructing a new expression that depends on the parameters in a linear way is described. To obtain the final solution, the least squares estimation of the main dependence linearized in terms of parameters is performed. The influence of various forms of noise imposed on the theoretical dependence on the approximations is modeled.

scholarly journals Comparison of Relaxation Modulus Converted from Frequency- and Time-Dependent Viscoelastic Functions through Numerical Methods

2018 ◽  
Vol 8 (12) ◽  
pp. 2447 ◽  
Author(s):  
Weiguang Zhang ◽  
Bingyan Cui ◽  
Xingyu Gu ◽  
Qiao Dong
Keyword(s):  
Least Squares ◽  
Collocation Method ◽  
Creep Compliance ◽  
Least Squares Method ◽  
Relaxation Modulus ◽  
Prony Series ◽  
Significant Difference ◽  
Time Region ◽  
The Difference ◽  
Reduced Time

Due to the difficulty of obtaining relaxation modulus directly from experiments, many interconversion methods from other viscoelastic functions to relaxation modulus were developed in previous years. The objectives of this paper were to analyze the difference of relaxation modulus converted from dynamic modulus and creep compliance and explore its potential causes. The selected methods were the numerical interconversions based on Prony series representation. For the dynamic to relaxation conversion, the time spectrum was determined by the collocation method. Meanwhile, for the creep to relaxation conversion, both the collocation method and least squares method were adopted to perform the Laplace transform. The results show that these two methods do not present a significant difference in estimating relaxation modulus. Their difference mostly exists in the transient reduced time region. Calculating the average of two methods is suggested to avoid great deviation of single experiment. To predict viscoelastic responses from creep compliance, the collocation method yields comparable results to the least squares method. Thus, simply-calculated collocation method may be preferable in practice. Further, the master curve pattern is sensitive to the Prony series coefficients. The difference in transient reduced time region may be attributed to the indeterminate Prony series coefficients.

scholarly journals IN INTERPOLATING THE VALUES OF FUNCTIONS SPECIFIED BY THE TABLE EFFECTIVENESS OF THE LEAST SQUARES METHOD

2020 ◽  
pp. 68-71
Author(s):  
М.Е. Eskaliyev ◽  
◽  
А.А. Masimgazieva ◽  
N.A. Nurgali ◽  
◽  
...  
Keyword(s):  
Least Squares ◽  
Least Squares Method ◽  
Main Idea ◽  
Gram Matrix ◽  
Method Of Least Squares ◽  
Newton Interpolation ◽  
Wide Range ◽  
Mathematical Formulas ◽  
The Difference ◽  
Interpolation Polynomials

The article provides a general algorithm of the method of least squares (OLS) for the compilation of a program account, taking into account the features of the Gram matrix. In fact, the difference and advantage of the OLS from the long-known Langrange and Newton interpolation polynomials is emphasized. Using the general MNC algorithm, the square version of the MNC is considered. The characteristic of the full algorithm of the square version is given using special selected mathematical formulas. The scope of OLS in household and practical computational problems is indicated. The application of the least squares method has a wide range, especially for geographical forecasts, hydrometeorological control, and dosage of geological resources. Therefore, for applied calculations, DVI is used for more accurate calculation of approximate values of functions that are suitable in some values and are presented in the form of tables. Its main idea is to create a function and correct deviations caused by errors made during measurement.

scholarly journals MACROECONOMIC VARIABLES AND VOLUME OF TRANSACTIONS ON TEHRAN STOCK EXCHANGE

2021 ◽  
Vol 33 (2) ◽  
pp. 163-173
Author(s):  
Farzaneh Haghighat Nia ◽  
Naser Shams Gharneh
Keyword(s):  
Exchange Rate ◽  
Least Squares ◽  
Analytical Method ◽  
Inflation Rate ◽  
Least Squares Method ◽  
Stock Exchange ◽  
Ordinary Least Squares ◽  
Macroeconomic Variables ◽  
The Relationship ◽  
Ordinary Least Squares Method

This paper examines the relationship between the volume of transactions and macroeconomic variables on the Tehran Stock Exchange. We are collect data for variables such as liquidity, inflation, exchange rate, the total value of imports and GDP for ten years period of 2009-2019. For analysis of data, have been used regression analytical method and ordinary least squares method (OLS) model. The results indicate that there are relationships between the macroeconomic variables of liquidity, inflation rate, and GDP with the volume of transactions. Therefore, the relationship between the volume of transactions with liquidity and GDP is positive and significant and with inflation is negative.

Monopulse Estimation of Unknown Polarization for Conformal Phased Array with Arbitrarily Oriented Dipoles

2021 ◽  
Author(s):  
Yuhao Deng ◽  
Julan Xie ◽  
Zishu He ◽  
Jun Li
Keyword(s):  
Least Squares ◽  
Phased Array ◽  
Least Squares Method ◽  
Likelihood Function ◽  
Hessian Matrix ◽  
Mean Square ◽  
Similar Technique ◽  
Dipole Orientation ◽  
Initial Direction ◽  
The Difference

Abstract In this paper, a novel monopulse estimator is proposed to surmount obstacles caused by unknown polarized pattern and the difference among each dipole orientation. Polarized pattern often alters the phased array response and we could hardly recover it if we known nothing about polarized parameters. The sum and difference beamforming of conformal phased array is affected due to the difference among each dipole orientation. Therefore the conventional monopulse estimator is dumped in this circumstance. The method proposed in this paper is a remarkable estimator based on maximum likelihood methodology. In this method, polarized parameters are considered as a part of desired signal and the least-squares solution of desired signal is obtained. With the desired signal solution, the likelihood function with respect to direction is derived at first. Then from the above, Jacobian and Hessian matrix of likelihood function is deduced. The boresight is considered as the initial direction value and the estimator of desired signal direction is obtained by Newton's formula. Finally, the polarized parameters are estimated by least-squares method using the direction estimator. The root-mean-square error (RMSE) of angle estimation is acceptable when prior polarized information is completely unknown. Polarized parameters are estimated by similar technique after we find out azimuth and elevation. Our research fills a gap of monopulse estimation with arbitrary polarization and diverse dipole arrangement.

THE INFLUENCE OF THE WORKING FACTOR AND CELL CONTENT ON THE PRECISION OF MICROSCOPIC COUNTS OF MILK SOMATIC CELLS1

1966 ◽  
Vol 29 (2) ◽  
pp. 49-52 ◽  
Author(s):  
R. Schneider ◽  
D. E. Jasper
Keyword(s):  
Least Squares ◽  
Cell Count ◽  
Inverse Relationship ◽  
Least Squares Method ◽  
The Other ◽  
Major Portion ◽  
Cell Content ◽  
Cell Counts ◽  
Count Range ◽  
The Relationship

Summary Variations in precision of the Breed method for cell counts in milk were investigated by utilizing different working factors (WF) for the same smear and by using the same WF over a major portion of the probable cell count range. A significant inverse relationship was found between precision and the WF. With a constant WF on the other hand, the precision of the count increased very significantly as the actual cell count increased. Formulas showing the relationship between the expected high and low for any given cell count were computed via the least squares method for a WF of 20,000. Evidence was presented that a WF of 5,000 or below would be necessary when a good estimate of cell content is important.

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