scholarly journals Time Scale in Least Square Method

2014 ◽  
Vol 2014 ◽  
pp. 1-6
Author(s):  
Özgür Yeniay ◽  
Öznur İşçi ◽  
Atilla Göktaş ◽  
M. Niyazi Çankaya
Keyword(s):  
Least Squares ◽  
Time Scale ◽  
Least Squares Method ◽  
Least Square Method ◽  
Forward Direction ◽  
Ordinary Least Squares ◽  
Least Square ◽  
Regression Equations ◽  
Nabla Derivative ◽  
Derivative Concept

Study of dynamic equations in time scale is a new area in mathematics. Time scale tries to build a bridge between real numbers and integers. Two derivatives in time scale have been introduced and called as delta and nabla derivative. Delta derivative concept is defined as forward direction, and nabla derivative concept is defined as backward direction. Within the scope of this study, we consider the method of obtaining parameters of regression equation of integer values through time scale. Therefore, we implemented least squares method according to derivative definition of time scale and obtained coefficients related to the model. Here, there exist two coefficients originating from forward and backward jump operators relevant to the same model, which are different from each other. Occurrence of such a situation is equal to total number of values of vertical deviation between regression equations and observation values of forward and backward jump operators divided by two. We also estimated coefficients for the model using ordinary least squares method. As a result, we made an introduction to least squares method on time scale. We think that time scale theory would be a new vision in least square especially when assumptions of linear regression are violated.

Fuzzy C-Regression Models

2013 ◽  
Vol 278-280 ◽  
pp. 1323-1326
Author(s):  
Yan Hua Yu ◽  
Li Xia Song ◽  
Kun Lun Zhang
Keyword(s):  
Linear Regression ◽  
Least Squares ◽  
Linear Models ◽  
Least Squares Method ◽  
Least Square Method ◽  
Least Square ◽  
Estimation Methods ◽  
Statistical Regression ◽  
Fuzzy Linear Regression ◽  
Fuzzy Degree

Fuzzy linear regression has been extensively studied since its inception symbolized by the work of Tanaka et al. in 1982. As one of the main estimation methods, fuzzy least squares approach is appealing because it corresponds, to some extent, to the well known statistical regression analysis. In this article, a restricted least squares method is proposed to fit fuzzy linear models with crisp inputs and symmetric fuzzy output. The paper puts forward a kind of fuzzy linear regression model based on structured element, This model has precise input data and fuzzy output data, Gives the regression coefficient and the fuzzy degree function determination method by using the least square method, studies the imitation degree question between the observed value and the forecast value.

Solitary waves of the RLW equation via least squares method

2021 ◽  
Vol 0 (0) ◽  
Author(s):  
Ozlem Ersoy Hepson ◽  
Idris Dag ◽  
Bülent Saka ◽  
Buket Ay
Keyword(s):  
Least Squares ◽  
Least Squares Method ◽  
Least Square Method ◽  
Least Square ◽  
Spline Functions ◽  
Algebraic Equations ◽  
B Spline ◽  
B Splines ◽  
Rlw Equation ◽  
Set Up

Abstract Integration using least squares method in space and Crank–Nicolson approach in time is managed to set up an algorithm to solve the RLW equation numerically. Trial functions in the least square method consist of a combination of the quartic B-spline functions. Integration of the RLW equation gives a system of algebraic equations. The solutions consisting of a combination of the quartic B-splines are given for some initial and boundary value problems of RLW equation.

A New Method to Identify the Preisach Distribution Function of Hysteresis

2005 ◽  
Vol 475-479 ◽  
pp. 2107-2110 ◽  
Author(s):  
Fan Li ◽  
Jian Qin Mao ◽  
Hai Shan Ding ◽  
Wen Bo Zhang ◽  
Hui Bin Xu ◽  
...  
Keyword(s):  
Distribution Function ◽  
Least Squares ◽  
Fuzzy Inference System ◽  
Fuzzy Inference ◽  
Least Squares Method ◽  
Input Sequence ◽  
Least Square Method ◽  
Least Square ◽  
New Method ◽  
Inference System

In this paper, a new method which combines the least square method with Tree-Structured fuzzy inference system is presented to approximate the Preisach distribution function. Firstly, by devising the input sequence and measure the output, discrete Preisach measure can be identified by the use of the least squares method. Then, the Preisach function can be obtained with Tree-Structured fuzzy inference system without any special smoothing means. So, this new method is not sensitive to noise, and is a universal approximator of the Preisach function. It collect the merit and overcome the deficiency of the existing methods.

scholarly journals A Comparative Analysis on Some Estimators of Parameters of Linear Regression Models in Presence of Multicollinearity

2018 ◽  
pp. 1-8
Author(s):  
Warha, Abdulhamid Audu ◽  
Yusuf Abbakar Muhammad ◽  
Akeyede, Imam
Keyword(s):  
Linear Regression ◽  
Least Squares ◽  
Regression Models ◽  
Mean Squared Error ◽  
Least Squares Method ◽  
Ordinary Least Squares ◽  
Least Square ◽  
Linear Regression Models ◽  
Independent Variables ◽  
Different Levels

Linear regression is the measure of relationship between two or more variables known as dependent and independent variables. Classical least squares method for estimating regression models consist of minimising the sum of the squared residuals. Among the assumptions of Ordinary least squares method (OLS) is that there is no correlations (multicollinearity) between the independent variables. Violation of this assumptions arises most often in regression analysis and can lead to inefficiency of the least square method. This study, therefore, determined the efficient estimator between Least Absolute Deviation (LAD) and Weighted Least Square (WLS) in multiple linear regression models at different levels of multicollinearity in the explanatory variables. Simulation techniques were conducted using R Statistical software, to investigate the performance of the two estimators under violation of assumptions of lack of multicollinearity. Their performances were compared at different sample sizes. Finite properties of estimators’ criteria namely, mean absolute error, absolute bias and mean squared error were used for comparing the methods. The best estimator was selected based on minimum value of these criteria at a specified level of multicollinearity and sample size. The results showed that, LAD was the best at different levels of multicollinearity and was recommended as alternative to OLS under this condition. The performances of the two estimators decreased when the levels of multicollinearity was increased.

Research and Experiment on Nonlinear Correction Algorithm of Metal Tube Rotameter

2011 ◽  
Vol 301-303 ◽  
pp. 1123-1127
Author(s):  
Gao Zhan Shen ◽  
Tao Zhang ◽  
Ying Xu ◽  
Yan Xing Wei
Keyword(s):  
Measurement Accuracy ◽  
Least Squares Method ◽  
Least Square Method ◽  
Ordinary Least Squares ◽  
Least Square ◽  
Metal Tube ◽  
Correction Algorithm ◽  
Improve Accuracy ◽  
Linear Correction ◽  
Ordinary Least Squares Method

The calibration curve of some metal tube rotameter has the characteristic of mutation. If the nonlinear least square method is still used as the method of linear correction, it will increase the measurement error and reduce the measurement accuracy. This paper presents a Division Ordinary Least Squares Method, which can reduce errors and improve accuracy. By the algorithm comparative experiment it can be proved that the method can improve the measurement accuracy.

An Application of Least Squares Method to the Solution of the Inverse Problem of Heat Conduction

1963 ◽  
Vol 85 (4) ◽  
pp. 378-379 ◽  
Author(s):  
Irving Frank
Keyword(s):  
Experimental Data ◽  
Inverse Problem ◽  
Heat Conduction ◽  
Least Squares ◽  
Heat Input ◽  
Least Squares Method ◽  
Least Square Method ◽  
The Body ◽  
Least Square

When the temperature of a body at some point is known, it is generally possible to determine the rate of heat input to the surface of the body. However, when the temperatures are determined experimentally, it will be found that there is some uncertainty in the solution for the rate of heat input. It is suggested that a least square method be used to determine the rate of heat input which best fits the experimental data.

scholarly journals Comparing ols and rank-based estimation techniques for production analysis: An application to Ghanaian maize farms.

2016 ◽  
Vol 10 (4-5) ◽  
pp. 125-130
Author(s):  
Henry De-Graft Acquah
Keyword(s):  
Least Squares ◽  
Production Function ◽  
Least Squares Method ◽  
Estimation Method ◽  
Ordinary Least Squares ◽  
Least Square ◽  
Least Squares Regression ◽  
Estimation Techniques ◽  
Production Analysis ◽  
Douglas Production Function

This paper introduces the rank-based estimation method to modelling the Cobb-Douglas production function as an alternative to the least squares approach. The intent is to demonstrate how a nonparametric regression based on a rank-based estimator can be used to estimate a Cobb-Douglas production function using data on maize production from Ghana. The nonparametric results are compared to common parametric specification using the ordinary least squares regression. Results of the study indicate that the estimated coefficients of the CobbDouglas Model using the Least squares method and the rank-based regression analysis are similar. Findings indicated that in both estimation techniques, land and Equipment had a significant and positive influence on output whilst agrochemicals had a significantly negative effect on output. Additionally, seeds which also had a negative influence on output was found to be significant in the robust rank-based estimation, but insignificant in the ordinary least square estimation. Both the least squares and rank-based regression suggest that the farmers were operating at an increasing returns to scale. In effect this paper demonstrate the usefulness of the rank-based estimation in production analysis. JEL CODE: Q18, D24, Q12, C1 and C67

scholarly journals European Option Based on Least-Squares Method under Non-Extensive Statistical Mechanics

Entropy ◽  
2019 ◽  
Vol 21 (10) ◽  
pp. 933
Author(s):  
Limin Liu ◽  
Yingying Cui
Keyword(s):  
Statistical Mechanics ◽  
Least Squares ◽  
Least Squares Method ◽  
Gaussian Model ◽  
Closed Form Solution ◽  
Least Square Method ◽  
Form Solution ◽  
Least Square ◽  
European Options ◽  
Non Gaussian

This paper is devoted to the study of the pricing of European options under a non-Gaussian model. This model follows a non-extensive statistical mechanics which can better describe the fractal characteristics of price movement in the financial market. Moreover, we present a simple but precise least-square method for approximation and obtain a closed-form solution of the price of European options. The advantages of this technique are illustrated by numerical simulation, which shows that the least-squares method is better compared with Borland’s two methods in 2002 and 2004.

Estimation of Parameters of Hyperbolic Functions with Additive Noise

2021 ◽  
Vol 105 ◽  
pp. 302-308
Author(s):  
Dmitriy V. Ivanov ◽  
Ilya L. Sandler ◽  
Natalya V. Chertykovtseva
Keyword(s):  
Differential Equations ◽  
Least Squares ◽  
Measurement Errors ◽  
Least Squares Method ◽  
Ordinary Least Squares ◽  
Least Square ◽  
Hyperbolic Function ◽  
Estimation Of Parameters ◽  
Hyperbolic Functions ◽  
Hyperbolic Sine

Hyperbolic functions are widely used to write solutions to ordinary differential equations and partial differential equations. These functions are nonlinear in parameters, which makes it difficult to estimate the parameters of these functions. In the paper, two-step algorithms for estimating the parameters of hyperbolic sine and cosine (sinh and cosh) in the presence of measurement errors are proposed. At the first step, the hyperbolic function is transformed into a linear difference equation (autoregression) of the second order. Estimation in the presence of noise of observation of autoregression parameters using ordinary least square (OLS) gives biased estimates. Modifications of the two-stage estimation algorithm based on the use of the method of total least squares (TLS) and the method of extended instrumental variables (EIV), hyperbolic sine and cosine in the presence of errors in measurements are proposed. Numerical experiments have shown that the accuracy of the parameter estimation using the proposed modifications is higher than the accuracy of the estimate obtained using the ordinary least squares method (OLS).

A Generalization of the Orthogonal Regression Technique for Life Cycle Inventory

2012 ◽  
Vol 3 (1) ◽  
pp. 51-71 ◽  
Author(s):  
Antonino Marvuglia ◽  
Maurizio Cellura ◽  
Marcello Pucci
Keyword(s):  
Life Cycle ◽  
Least Squares ◽  
Least Squares Method ◽  
Linear Equations ◽  
Mathematical Formulation ◽  
Ordinary Least Squares ◽  
Least Square ◽  
Regression Problems ◽  
Whole Life Cycle ◽  
Interesting Development

Life cycle assessment (LCA) is a method used to quantify the environmental impacts of a product, process, or service across its whole life cycle. One of the problems occurring when the system at hand involves processes delivering more than one valuable output is the apportionment of resource consumption and environmental burdens in the correct proportion amongst the products. The mathematical formulation of the problem is represented by the solution of an over-determined system of linear equations. The paper describes the application of an iterative algorithm for the implementation of least square regression to solve this over-determined system directly in its rectangular form. The applied algorithm dynamically passes from an Ordinary Least Squares (OLS) problem to the regression problems known as Total Least Squares (TLS) and Data Least Squares (DLS). The obtained results suggest further investigations. In particular, the so called constrained least squares method is identified as an interesting development of the methodology.

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