scholarly journals Asymptotic normality of a simple linear EV regression model with martingale difference errors

Filomat ◽  
2014 ◽  
Vol 28 (9) ◽  
pp. 1817-1825
Author(s):  
Guo-Liang Fan ◽  
Tian-Heng Chen
Keyword(s):  
Regression Model ◽  
Least Squares ◽  
Measurement Errors ◽  
Least Squares Method ◽  
Error Variance ◽  
Martingale Difference ◽  
Errors In Variables ◽  
Ev Regression Model ◽  
Biased Estimators ◽  
Better Than

This paper considers the estimation of a linear EV (errors-in-variables) regression model under martingale difference errors. The usual least squares estimations lead to biased estimators of the unknown parametric when measurement errors are ignored. By correcting the attenuation we propose a modified least squares estimator for a parametric component and construct the estimators of another parameter component and error variance. The asymptotic normalities are also obtained for these estimators. The simulation study indicates that the modified least squares method performs better than the usual least squares method.

scholarly journals A Least Squares Method for Variance Estimation in Heteroscedastic Nonparametric Regression

2014 ◽  
Vol 2014 ◽  
pp. 1-14
Author(s):  
Yuejin Zhou ◽  
Yebin Cheng ◽  
Tiejun Tong
Keyword(s):  
Least Squares ◽  
Nonparametric Regression ◽  
Variance Estimation ◽  
Least Squares Method ◽  
Asymptotic Properties ◽  
Error Variance ◽  
Simulation Studies ◽  
Least Squares Estimators ◽  
Slope Estimator ◽  
Better Than

Interest in variance estimation in nonparametric regression has grown greatly in the past several decades. Among the existing methods, the least squares estimator in Tong and Wang (2005) is shown to have nice statistical properties and is also easy to implement. Nevertheless, their method only applies to regression models with homoscedastic errors. In this paper, we propose two least squares estimators for the error variance in heteroscedastic nonparametric regression: the intercept estimator and the slope estimator. Both estimators are shown to be consistent and their asymptotic properties are investigated. Finally, we demonstrate through simulation studies that the proposed estimators perform better than the existing competitor in various settings.

Asymptotic for LS estimators in the EV regression model for dependent errors

Filomat ◽  
2017 ◽  
Vol 31 (15) ◽  
pp. 4845-4856
Author(s):  
Konrad Furmańczyk
Keyword(s):  
Regression Model ◽  
Functional Dependence ◽  
Dependent Data ◽  
Errors In Variables ◽  
Mixing Conditions ◽  
Asymptotic Results ◽  
Dependence Measure ◽  
Wide Range ◽  
Ev Regression Model ◽  
Linear And Nonlinear

We study consistency and asymptotic normality of LS estimators in the EV (errors in variables) regression model under weak dependent errors that involve a wide range of linear and nonlinear time series. In our investigations we use a functional dependence measure of Wu [16]. Our results without mixing conditions complete the known asymptotic results for independent and dependent data obtained by Miao et al. [7]-[10].

scholarly journals The Impact of Public Debt on the Economic Growth of Jordan: An Empirical Study (2000- 2015)

2017 ◽  
Vol 6 (2) ◽  
pp. 114 ◽  
Author(s):  
Tawfiq Ahmad Mousa ◽  
Abudallah. M. LShawareh
Keyword(s):  
Economic Growth ◽  
Empirical Study ◽  
Regression Model ◽  
Least Squares ◽  
Public Debt ◽  
Least Squares Method ◽  
Negative Impact ◽  
External Debt ◽  
Using Data ◽  
The Impact

In the last two decades, Jordan’s economy has been relied on public debt in order to enhance the economic growth. As such, an understanding  of the dynamics between public debt and economic growth is very important in addressing the obstacles to economic growth. The study investigates the impact of public debt on economic growth using data from 2000 to 2015. The study employs least squares method and regression model to capture the impact of public debt on economic growth. The results of the analysis indicate that there is a negative impact of total public debt, especially the external debt on economic growth. 

scholarly journals Method of determining the distance to the object by analyzing its image blur

Vestnik MGSU ◽  
2015 ◽  
pp. 140-151 ◽  
Author(s):  
Aleksey Alekseevich Loktev ◽  
Daniil Alekseevich Loktev
Keyword(s):  
Least Squares ◽  
Statistical Approach ◽  
Evaluation Method ◽  
Least Squares Method ◽  
Focal Length ◽  
Error Variance ◽  
Method Of Least Squares ◽  
Automated Control ◽  
Image Blur

In modern integrated monitoring systems and systems of automated control of technological processes there are several essential algorithms and procedures for obtaining primary information about an object and its behavior. The primary information is characteristics of static and moving objects: distance, speed, position in space etc. In order to obtain such information in the present work we proposed to use photos and video detectors that could provide the system with high-quality images of the object with high resolution. In the modern systems of video monitoring and automated control there are several ways of obtaining primary data on the behaviour and state of the studied objects: a multisensor approach (stereovision), building an image perspective, the use of fixed cameras and additional lighting of the object, and a special calibration of photo or video detector.In the present paper the authors develop a method of determining the distances to objects by analyzing a series of images using depth evaluation using defocusing. This method is based on the physical effect of the dependence of the determined distance to the object on the image from the focal length or aperture of the lens. When focusing the photodetector on the object at a certain distance, the other objects both closer and farther than a focal point, form a spot of blur depending on the distance to them in terms of images. Image blur of an object can be of different nature, it may be caused by the motion of the object or the detector, by the nature of the image boundaries of the object, by the object’s aggregate state, as well as by different settings of the photo-detector (focal length, shutter speed and aperture).When calculating the diameter of the blur spot it is assumed that blur at the point occurs equally in all directions. For more precise estimates of the geometrical parameters determination of the behavior and state of the object under study a statistical approach is used to determine the individual parameters and estimate their accuracy. A statistical approach is used to evaluate the deviation of the dependence of distance from the blur from different types of standard functions (logarithmic, exponential, linear). In the statistical approach the evaluation method of least squares and the method of least modules are included, as well as the Bayesian estimation, for which it is necessary to minimize the risks under different loss functions (quadratic, rectangular, linear) with known probability density (we consider normal, lognormal, Laplace, uniform distribution). As a result of the research it was established that the error variance of a function, the parameters of which are estimated using the least squares method, will be less than the error variance of the method of least modules, that is, the evaluation method of least squares is more stable. Also the errors’ estimation when using the method of least squares is unbiased, whereas the mathematical expectation when using the method of least modules is not zero, which indicates the displacement of error estimations. Therefore it is advisable to use the least squares method in the determination of the parameters of the function.In order to smooth out the possible outliers we use the Kalman filter to process the results of the initial observations and evaluation analysis, the method of least squares and the method of least three standard modules for the functions after applying the filter with different coefficients.

scholarly journals GM(1,1;λ) with Constrained Linear Least Squares

Axioms ◽  
2021 ◽  
Vol 10 (4) ◽  
pp. 278
Author(s):  
Ming-Feng Yeh ◽  
Ming-Hung Chang
Keyword(s):  
Least Squares ◽  
Least Squares Method ◽  
Model Fitting ◽  
Ordinary Least Squares ◽  
Linear Least Squares ◽  
Unknown Parameters ◽  
Constrained Problems ◽  
Linear Least Squares Problems ◽  
Ordinary Least Squares Method ◽  
Better Than

The only parameters of the original GM(1,1) that are generally estimated by the ordinary least squares method are the development coefficient a and the grey input b. However, the weight of the background value, denoted as λ, cannot be obtained simultaneously by such a method. This study, therefore, proposes two simple transformation formulations such that the unknown parameters, and can be simultaneously estimated by the least squares method. Therefore, such a grey model is termed the GM(1,1;λ). On the other hand, because the permission zone of the development coefficient is bounded, the parameter estimation of the GM(1,1) could be regarded as a bound-constrained least squares problem. Since constrained linear least squares problems generally can be solved by an iterative approach, this study applies the Matlab function lsqlin to solve such constrained problems. Numerical results show that the proposed GM(1,1;λ) performs better than the GM(1,1) in terms of its model fitting accuracy and its forecasting precision.

Evaluation of industry tendencies in Uzbekistan

2020 ◽  
Vol 8 ◽  
Author(s):  
Radjabov Bunyod Abduhalilovich
Keyword(s):  
Regression Model ◽  
Least Squares ◽  
Industrial Production ◽  
Industrial Development ◽  
Least Squares Method ◽  
Development Trends ◽  
Industry Development

The article proposes a method for assessing trends in industrial development in Uzbekistan. The least-squares method of the regression model was used to estimate industry development trends. Development trends are assessed based on the index of change in the final and theoretical values of industrial production.

scholarly journals A Monograph on Nonlinear Regression Models

2018 ◽  
Vol 7 (4.10) ◽  
pp. 543
Author(s):  
B. Mahaboob ◽  
B. Venkateswarlu ◽  
C. Narayana ◽  
J. Ravi sankar ◽  
P. Balasiddamuni
Keyword(s):  
Regression Model ◽  
Least Squares ◽  
Nonlinear Regression ◽  
Nonlinear Models ◽  
Nonlinear Least Squares ◽  
Error Variance ◽  
Ordinary Least Squares ◽  
Parameter Estimates ◽  
Nonlinear Regression Model ◽  
Nonlinear Regression Models

This research article uses Matrix Calculus techniques to study least squares application of nonlinear regression model, sampling distributions of nonlinear least squares estimators of regression parametric vector and error variance and testing of general nonlinear hypothesis on parameters of nonlinear regression model. Arthipova Irina et.al [1], in this paper, discussed some examples of different nonlinear models and the application of OLS (Ordinary Least Squares). MA Tabati et.al (2), proposed a robust alternative technique to OLS nonlinear regression method which provide accurate parameter estimates when outliers and/or influential observations are present. Xu Zheng et.al [3] presented new parametric tests for heteroscedasticity in nonlinear and nonparametric models.  

The Optimization of the PID Controller Using the Least Squares Method and the Improved Lbest PSO Algorithm

2013 ◽  
Vol 397-400 ◽  
pp. 1296-1303 ◽  
Author(s):  
Chuan Gui Yang ◽  
Zhao Jun Yang ◽  
Fei Chen ◽  
Yan Zhu ◽  
Ying Nan Kan ◽  
...  
Keyword(s):  
Least Squares ◽  
Pid Controller ◽  
Least Squares Method ◽  
Dynamic Performance ◽  
Pso Algorithm ◽  
Pid Tuning ◽  
Loading System ◽  
Hydraulic Servo ◽  
Tuning Scheme ◽  
Better Than

A self-adaptive PID tuning scheme is presented for the electro-hydraulic servo loading system. It requires the least squares method to identify the parameters of the transfer function of the electro-hydraulic servo loading system and utilizes the improved lbest PSO algorithm to optimize the PID controller. The scheme can provide the optimal PID parameters so that the dynamic performance and stability of the electro-hydraulic servo loading system are improved. Results show the fact that the dynamic performance and stability of the system are improved by the scheme. And in terms of optimization of PID controller, the improved lbest PSO algorithm is better than the lbest PSO algorithm and Ziegler-Nichols method.

scholarly journals TREATMENT OF GEODETIC SURVEY DATA AS FUZZY VECTORS

2015 ◽  
Vol XL-3/W3 ◽  
pp. 29-33
Author(s):  
G. Navratil ◽  
E. Heer ◽  
J. Hahn
Keyword(s):  
Normal Distribution ◽  
Least Squares ◽  
Survey Data ◽  
Measurement Errors ◽  
Least Squares Method ◽  
Measurement Data ◽  
Geodetic Survey ◽  
Present Measurement ◽  
A Value ◽  
Light Signals

Geodetic survey data are typically analysed using the assumption that measurement errors can be modelled as noise. The least squares method models noise with the normal distribution and is based on the assumption that it selects measurements with the highest probability value (Ghilani, 2010, p. 179f). There are environment situations where no clear maximum for a measurement can be detected. This can happen, for example, if surveys take place in foggy conditions causing diffusion of light signals. This presents a problem for automated systems because the standard assumption of the least squares method does not hold. A measurement system trying to return a crisp value will produce an arbitrary value that lies within the area of maximum value. However repeating the measurement is unlikely to create a value following a normal distribution, which happens if measurement errors can be modelled as noise. In this article we describe a laboratory experiment that reproduces conditions similar to a foggy situation and present measurement data gathered from this setup. Furthermore we propose methods based on fuzzy set theory to evaluate the data from our measurement.

Fuzzy Regression Model Based on Geometric Centroid and Incentre Points and Application to Performance Evaluation

2020 ◽  
Vol 28 (02) ◽  
pp. 269-288
Author(s):  
Yanbing Gong ◽  
Lin Xiang ◽  
Gaofeng Liu
Keyword(s):  
Regression Model ◽  
Least Squares ◽  
Least Squares Method ◽  
Estimation Error ◽  
Triangular Fuzzy Number ◽  
Fuzzy Regression ◽  
Distance Method ◽  
Fuzzy Input ◽  
Fuzzy Regression Model ◽  
Fuzzy Linear Regression Model

Fuzzy regression model is developed to construct the relationship between independent variable and dependent variable in a fuzzy environment. In order to increase the explanatory performance of fuzzy regression model, the least-squares method usually is applied to determine the numeric coefficients based on the concept of distance. In this paper, we consider the fuzzy linear regression model with fuzzy input, fuzzy output and crisp parameters and introduce a new distance based on the geometric centroid and incentre points (GCIP) of triangular fuzzy number, merge least-squares method with the new GCIP distance and propose least-squares GCIP distance method. Finally, an example of employee job performance is given to illustrate the effectiveness and feasibility of the method. Comparisons with existing methods show that total estimation error using the same distance criterion, the explanatory performance of the GCIP method is satisfactory, and the calculation is relatively simple.

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